Episodic Exploration for Deep Deterministic Policies:
An Application to StarCraft Micromanagement Tasks
Abstract
We consider scenarios from the realtime strategy game StarCraft as new benchmarks for reinforcement learning algorithms. We propose micromanagement tasks, which present the problem of the shortterm, lowlevel control of army members during a battle. From a reinforcement learning point of view, these scenarios are challenging because the stateaction space is very large, and because there is no obvious feature representation for the stateaction evaluation function. We describe our approach to tackle the micromanagement scenarios with deep neural network controllers from raw state features given by the game engine. In addition, we present a heuristic reinforcement learning algorithm which combines direct exploration in the policy space and backpropagation. This algorithm allows for the collection of traces for learning using deterministic policies, which appears much more efficient than, for example, greedy exploration. Experiments show that with this algorithm, we successfully learn nontrivial strategies for scenarios with armies of up to agents, where both Qlearning and REINFORCE struggle.
1 Introduction
StarCraft^{1}^{1}1StarCraft and its expansion StarCraft: Brood War
are trademarks of Blizzard Entertainment is a
realtime strategy game in which each player must build an army and
control individual units to destroy the opponent’s army. As of
today, StarCraft is considered one of the most difficult games for
computers, and the best bots only reach the level of high amateur
human
players^{2}^{2}2http://webdocs.cs.ualberta.ca/c̃david/starcraftaicomp/report2015.shtml#mvm
(retrieved
on August rd, 2016).. The main difficulty comes from the need to
control a large number of units in a wide, partially observable
environment. This implies, in particular, extremely large state and
action spaces: in a typical game, there are at least
possible states (for reference, the game of Go has about
states) and the joint action space is in , with a peak number of units of about
[36]. From a machine learning point of
view, StarCraft provides an ideal environment to study the control of
multiple agents at large scale, and also an opportunity to define
tasks of increasing difficulty, from micromanagement, which
concerns the shortterm, lowlevel control of fighting units during
battles, to longterm strategic and hierarchical planning under
uncertainty. While building a controller for the full game based on
machine learning is outofreach for current methods, we propose, as a
first step, to study reinforcement learning algorithms in
micromanagement scenarios in StarCraft.
Both the work on Atari games [19] and the recent Minecraft scenarios studied by researchers [1, 22] focus on the control of a single agent, with a fixed, limited set of actions. Coherently controlling multiple agents (units) is the main challenge of reinforcement learning for micromanagement tasks. This comes with two main difficulties. The first difficulty is to efficiently explore the large action space. The implementation of a coherent strategy requires the units to take actions that depend on each other, but it also implies that any small alteration of a strategy must be maintained for a sufficiently long time to properly evaluate the longterm effect of that change. In contrast to this requirement of consistency in exploration, the reinforcement learning algorithms that have been successful in training deep neural network policies such as Qlearning [44, 34] and REINFORCE [46, 7], perform exploration by randomizing actions. In the case of micromanagement, randomizing actions mainly disorganizes the units, which then rapidly lose the battle without collecting relevant feedback. The second major difficulty of micromanagement scenarios is that there is no obvious way to parameterize the policy given the state and the actions, because some actions describe a relation between entities of the state, e.g., (unit A, attack, unit B) or (unit A, move, position B) and are not restricted to a few constant symbols such as “move left” or “move right”. The approach of “learning directly from pixels”, in which the pixel input is fed to a multiclass convolutional neural network, was successful in Atari games [20]. However, pixels only capture spatial relationships between units. These are only parts of the relationships of interest, and more generally this kind of multiclass architecture cannot evaluate actions that are parameterized by an entity of the state.
The contribution of this paper is twofold. First, we propose several micromanagement tasks from StarCraft (Section 3), then we describe our approach to tackle them and evaluate well known reinforcement learning algorithms on these tasks (Section 4), such as Qlearning and REINFORCE (Subsection 4.1). In particular, we present an approach of greedy inference to break out the complexity of taking the actions at each step (Subsection 4.2). We also describe the features used to jointly represent states and actions, as well as a deep neural network model for the policy (Section 5). Second, we propose a heuristic reinforcement learning algorithm to address the difficulty of exploration in these tasks (Section 6). To avoid the pitfalls of exploration by taking randomized actions at each step, this algorithm explores directly in policy space, by randomizing a small part of the deep network parameters at the beginning of an episode and running the altered, deterministic, policy thoughout the whole episode. Parameter updates are performed using a heuristic approach combining gradientfree optimization for the randomized parameters, and plain backpropagation for the others. Compared to algorithms for efficient direct exploration in parameter space (see e.g., [18, 27, 37, 25]), the novelty of our algorithm is to mix exploration through parameter randomization and plain gradient descent. Parameter randomization is efficient for exploration but learns slowly with a large number of parameters, whereas gradient descent does not take part in any exploration but can rapidly learn models with millions of parameters.
2 Related work
Multiagent reinforcement learning has been an active area of research (see e.g., [4]). Most of the focus has been on learning agents in competitive environments with adaptive adversaries (e.g., [15, 13, 40]). Some work has looked at learning control policies for individual agents in a collaborative setting with communication constraints [38, 3], with applications such as soccer robot control [31], and methods such as hierarchical reinforcement learning for communicating highlevel goals [12], or learning an efficient communication protocol [32]. While the decentralized control framework is most likely relevant for playing full games of StarCraft, here we avoid the difficulty of imperfect information, therefore we use the multiagent structure only as a means to structure the action space. As in the approach of [17] with reinforcement learning for structured output prediction, we use a greedy sequential inference scheme at each time frame: each unit decides on its action based solely on the state combined with the actions of units that came before it in the sequence.
Algorithms that have been used to train deep neural network controllers in reinforcement learning include Qlearning [44, 20], the method of temporal differences [33, 39], policy gradient and their variants [46, 7], and actor/critic architectures [2, 29, 28]. Except for the deterministic policy gradient (DPG) [29], these algorithms rely on randomizing the actions at each step for exploration. DPG collects traces by following deterministic policies that remain constant throughout an episode, but can only be applied when the action space is continuous. Our work is most closely related to works that explore the parameter space of policies rather than the action space. Several approaches have been proposed that randomize the parameters of the policy at the beginning of an episode and run a deterministic policy throughout the entire episode, borrowing ideas from gradientfree optimization (see e.g., [18, 27, 37]). However, these algorithms rely on gradientfree optimization for all parameters, which does not scale well with the number of parameters. Osband et al. [25] describe another type of algorithm where the parameters of a deterministic policy are randomized at the beginning of an episode, and learn a posterior distribution over the parameters as in Thomson sampling [41]. Their algorithm is particularly suitable for problems in which depthfirst search exploration is efficient, so their motivation is very similar to ours. Their approach was proved to be efficient, but applies only to linear functions and scales quadratically with the number of parameters. The bootstrapped deep Qnetworks (BDQN) [24] are a practical implementation of the ideas of [25] for deep neural networks. However, BDQN still performs exploration in the action space at the beginning of the training, and there is no randomization of the parameters. Instead, several versions of the last layer of the deep neural network controller are maintainted, and one of them is used alternatively during an entire episode to generate diverse traces and perform Qlearning updates. In contrast, we randomize the parameters of the last layer once at the beginning of an episode, and contrarily to Qlearning, our algorithm does not rely on the estimation of the stateaction value function.
In the context of StarCraft micromanagement, a large spectrum of AI approaches have been studied. There has been work on Bayesian fusion of handdesigned influence maps [36], fast heuristic search (in a simplified simulator of battles without collisions) [5], and even evolutionary optimization [16]. Closer to this work, [45] successfully applied tabular Qlearning [44] and SARSA [34], with and without experience replay (“eligility traces”), with a reward similar to the one used in several of our experiments. However, the action space was reduced to precomputed “metaactions”: fight and retreat, and the features were handcrafted. None of these approaches are used as is in existing StarCraft bots, mainly for a lack of robustness to all micromanagement scenarios that can happen in a full game, for a lack of completeness (both can be attributed to handcrafting), or for a lack of computational efficiency (speed). For a more detailed overview of AI research on StarCraft, the reader should consult [23].
3 StarCraft micromanagement scenarios
We focus on micromanagement, which consists of optimizing each unit’s actions during a battle. The tasks presented in this paper represent only a subset of the complexity of playing StarCraft. As StarCraft is a realtime strategy (RTS) game, actions are durative (are not fully executed on the next frame), and there are approximately 24 frames per second. As we take an action for each unit every few frames (e.g. every 9 frames here, see A.1 in Appendix for more details), we only consider actions that can be executed in this time frame, which are: the 8 move directions, holding the current position, an attack action for each of the existing enemy units. In all tasks, we control all units from one side, and the opponent (builtin AI in the experiments) is attacking us:

m5v5 is a task in which we control 5 Marines (ranged ground unit), against 5 opponent Marines. A good strategy here is to focus fire, by whatever means. For example, we can attack the weakest opponent unit (the unit with the least remaining life points), with tie breaking, or attack the closest to the group.

m15v16: same as above, except we have 15 Marines and the opponent has 16. A good strategy here is also to focus fire, while avoiding “overkill” (spread the damage over several units if the focus firing is enough to kill one of the opponent’s unit). A Marine has 40 hit points, and can hit for 6 hit points every 15 frames.

dragoons_zealots: symmetric armies with two types of units: 3 Zealots (melee ground unit) and 2 Dragoons (ranged ground unit). Here a strategy requires to focus fire, and if possible to 1) not spend too much time having the Zealots walk instead of fight, 2) focus the Dragoons (which receive full damage from both Zealots and Dragoons while inflicting only half damage on Zealots).

w15v17: we control 15 Wraiths (ranged flying unit) while the opponent has 17. Flying units have no “collision”, so multiple units can occupy the same tile. Here more than anywhere, it is important not to “overkill”: Wraiths have 120 hit points, and can hit for 20 damage on a 22 frame cooldown. As there is no collision, moving is easier.

other mXvY or wXvY scenarios. The 4 scenarios above are the ones on which we train our models, but they can learn strategies that overfit a given number of units, so we have similar scenarios but with different numbers of units (on each side).
For all these scenarios, a human expert can win 100% of the time against the builtin AI, by moving away units that are hurt (thus conserving firepower) and with proper focus firing.
4 Framework: RL and multiple units
We now describe the notation and definition underlying the algorithms Qlearning and policy gradient (PG) used as baselines here. We then reformulate the joint inference over the potential actions for different units as a greedy inference which reduces to a usual MDP with more states but fewer actions per state. We then show how we normalize cumulative rewards at each state in order to keep rewards in the full interval , during an entire episode, even when units disappear.
4.1 Preliminaries: Qlearning and REINFORCE
Notation
The environment is approximated as an MDP, with a finite set of states denoted by . Each state has a set of units , and a policy has to issue a command to each of them. The set of commands is finite. An action in that MDP is represented as a sequence of (unit, command) pairs such that . denotes the number of units in state and the set of actions in state . We denote by the transition probability of the MDP and by the probability distribution of initial states. When there is a transition from state to a state , the agent receives the reward , where is the reward function. We assume that commands are received and executed concurrently, so that the order of commands in an action does not alter the transition probabilities. Finally, we consider the episodic reinforcement learning scenario, with finite horizon and undiscounted rewards. The learner has to learn a (stochastic) policy , which defines a probability distribution over actions in for every . The objective is to maximize the expected undiscounted cumulative reward over episodes , where the expectation is taken with respect to , and .
Qlearning
The Qlearning algorithm in the finitehorizon setting learns an actionvalue function by solving the Bellman equation
(1) 
where is the stateaction value function at stage of an episode, and by convention. is also whenever a terminal state is reached, and transitions from a terminal state only go to the same terminal state.
Training is usually carried out by collecting traces using greedy exploration: at state and stage , an action in is chosen with probability , or an action in is chosen uniformly at random with probability . In practice, we use stationary functions (i.e., ), which are neural networks, as described in Section 5. Training is carried out using the standard online update rule for Q learning with function approximation (see e.g., [20]), which we apply in minibatches (see Section A.2 for more details).
This training phase is distinct from the test phase, in which we record the average cumulative reward of the deterministic policy .
Reinforce
The algorithm REINFORCE belongs to the family of policy gradient algorithms [35]. Given a stochastic policy parameterized by , learning is carried out by generating traces by following the current policy. Then, stochastic gradient updates are performed, using the gradient estimate:
(2) 
We use a Gibbs policy (with temperature parameter ) as the stochastic policy:
(3) 
where is a neural network with paramters that gives a realvalued score to each (state, action) pair. For testing, we use the deterministic policy .
4.2 The MDP for greedy inference
One way to break out the complexity of jointly infering the commands to each individual unit is to perform greedy inference at each step: at each state, units choose a command one by one, knowing the commands that were previously taken by other units. Learning a greedy policy boils down to learning a policy in another MDP with fewer actions per state but exponentially more states, where the additional states correspond to the intermediate steps of the greedy inference. This reduction was previously proposed in the context of structured prediction by Maes et al. [17], who proved that an optimal policy in this new MDP has the same cumulative reward as an optimal policy in the original MDP.
A natural way to define the MDP associated with greedy inference, hereafter called greedy MDP, is to define the set of atomic actions of the greedy policy as all possible (unit, command) pairs for the units whose command is still not decided. This would lead to an inference with quadratic complexity with respect to the number of units, which is undesirable.
Another possibility is to first choose a unit, then a command to apply to that unit, which yields an algorithm with steps for state . Since the commands are executed concurrently by the environment after all commands have been decided, the cumulative reward does not depend on the order in which we choose the units. Going further, we can let the environment in the greedy MDP choose the next unit, for instance, uniformly at random among remaining units. The resulting inference has a complexity that is linear in the number of units. More formally, using the notation to denote the first (unit, command) pairs of an action (with the convention ), the state space of the greedy MDP is defined by
The action space of each state is constant and equal to the set of commands . Moreover, for each state of the original MDP, any action , the transition probabilities in the greedy MDP are defined by
(4)  
(5) 
Finally, using the same notation as above, the reward function between states that represent intermediate steps of the algorithm is and the last unit to play receives the reward:
It can be shown that an optimal policy for this greedy MDP chooses actions that are optimal for the original MDP, because the immediate reward in the original MDP does not depend on the order in which the actions are taken. This result only applies if the family of policies has enough capacity. In practice, some ordering may be easier to learn than others, but we did not investigate this issue because the gain, in terms of computation time, of the random ordering was critical for the experiments.
4.3 Normalized cumulative rewards
Immediate rewards are necessary to provide feedback that guides exploration. In the case of micromanagement, a natural reward signal is the difference between damage inflicted and incurred between two states. The cumulative reward over an episode is the total damage inflicted minus the total damage incurred along the episode. However, the scale of this quantity heavily depends on the number of units (both our units and enemy units) that are present in the state, a quantity which significantly decreases along an episode. Without proper normalization with respect to the number of units in the current state, learning will be artificially biased towards the large immediate rewards at the beginning of the episode.
We present a simple method to normalize the immediate rewards on a perstate basis, assuming that a scale factor is available to the learner – it can be as simple as the number of units. Then, instead of considering cumulative rewards from a starting state , we define normalized cumulative rewards as the following recursive computation over an episode:
These normalized rewards maitain the invariant ; but more importantly, the normalization can be applied to the Bellman equation (1), which becomes
The stochastic gradient updates for Qlearning can easily be modified accordingly, as well as the gradient estimate in REINFORCE (2) in which we replace by .
One way to look at this normalization process is to consider that the reward is , and plays the role of an (adaptive) discount factor, which is chosen to be at most , and strictly smaller than 1 when the number of units change.
5 Features and model for micromanagement in StarCraft
The features and models we use are intended to test the ability of RL algorithms to learn strategies when given as little prior knowledge as possible. We voluntarily restrict ourselves to raw features extracted from the state description given by the game engine, without encoding any prior knwoledge of the game dynamics. This contrast with prior work on Qlearning for micromanagement such as [45], which use features such as the expected inflicted damage. We do not allow ourselves to encode the effect of an attack action on the hit points of the attacked unit; we do not, either, construct crossfeatures nor provide any relevant discretization of the features (e.g., whether unit A is in the range of unit B). The only transformation of the raw features we perform is the computation of distances between units and (between) targets of commands.
We represent a state as a sequence of feature vectors, one feature vector per unit (ally or enemy) in the state. We remind that each state in the greedy MDP is a tuple and an action in that MDP corresponds to a command that shall execute. At each frame and for each unit, the commands we consider are (1) attack a given enemy unit, and (2) move to a specific position. In order to reduce the number of possible move commands, we only consider move commands, which either correspond to a move in one of the 8 basic directions, or staying at the same position.
Attack commands are nontrivial to featurize because the model needs be able to solve the reference from the identifiers of the units that attack or are attacked to their corresponding attributes. In order to solve this issue, we construct a joint state/action feature representation in which the unit positions (coordinates on the map) are indirectly used to refer to the units. We now detail the feature representation we use and the neural network model.
5.1 Raw state information and featurization
For each unit (ally or enemy), the following attributes are extracted from the raw state description given by the game engine:

Unit attributes: the unit type, its coordinates on the map (pos), the remaining number of hit points (hp), the shield, which corresponds to additional hit points that can be recovered when the unit is not attacked, and, finally the weapon cooldown (cd, number of frames to wait to be able to inflict damage again). An additional flag enemy is used to distinguish between our units and enemy units.

Two attributes that describe the command that is currently executed by the unit. First, the target attribute, which, if not empty, is the identifier of the enemy unit currently under attack. This identifier is an integer that is attributed arbitrarily by the game engine, and does not convey any semantics. We do not encode directly this identifier in the model, but rather only use the position of the (target) unit (as we describe below in the distance features).
The second attribute, target_pos gives the coordinates on the map of the position of the target (the desired destination if the unit is currently moving, or the position of the target if the latter is not empty). These fields are available for both ally and enemy units; from these we infer the current command cur_cmd that the unit currently performs.
In order to assign a score to a tuple where is a candidate command for , the joint representation is defined as sequence of feature vectors, one for each unit . The feature vector for unit , which is denoted by , is a joint representation of together with its next command next_cmd if it has already been decided (i.e. if is an ally unit whose next command is in ), and of the command that is evaluated for . All commands have a field act_type (attack or move) and a field target_pos. If we want to featurize a command that is not available for a given unit, such as the next command for an enemy unit, we set act_type to a specific “no command” value and target_pos to the unit position.
Given , the vector contains the features described below. We use an objectoriented programming notation “a.b” to refer to the value of attribute b of a:
Nonpositional features
(boolean), (categorical, onehot encoding), , , (all three realvalued), (categorical, onehot encoding), , . At this stage, we do not encode the type of the command act_type, which is another input to the network (see Section 5.2).
Relative distance features
for
and
. These features,
in particular, encode which unit is because the distance
between positions is . They also encode which unit is the target of
the command, and which units have the same target. This encoding is
unambiguous as long as units cannot have the same position, which is
not true for flying units (units have the same position, either as
actor or target of a command, will be treated as the same). In
practice however, the confusion of units did not seem to be a major
issue since units rarely have exactly the same position.
Finally, the full (state, action) tuple of the greedy MDP is represented by an matrix, in which the th row is . The model, which we describe below, deals with the variablesize input with global pooling operations.
5.2 Deep Neural Network model
As we shall see in Section 6, we consider
stateaction scoring functions of the form
, where
is a vector in and is an deep network with parameters which
embeds the state and command of the greedy MDP into .
The embedding network takes as input a matrix, which we describe below, and operates in two steps:
(1) Cross featurization and pooling in this step, each row goes through a 2layer neural network, with each layer of width , with an ELU nonlinearity [6] for the first layer and hyperbolic tangeants as final activation functions. The resulting matrix is then aggreated into two different vectors of size : the first one by taking the mean value of each column (average pooling), and the second one by taking the maximum (max pooling). The two vectors are then concatenated and yield a dimensional vector for the next step. We can note that this final fixedlength representation is invariant to the ordering of rows of the original matrix.
(2) Scoring with respect to action type the dimensional vector is then concatenated with the type of action (onehot encoding of two values: attack or move). The concatenation goes through a 2layer network with activation units at each layer. The first nonlinearity is an ELU, while the second is a rectifier linear unit (ReLU).
The rationale behind this model is that it can represent the answer to a variety of question regarding the relationship between the candidate command and the state, such as: what is the type of unit of the command’s target? How many damages shall be inflicted? How many units already have the same target? How many units are attacking ?
Yet, in order to answer these questions, the learner must perform the appropriate crossfeatures and paramter updtaes from the reinforcement signal alone, so the learning task is nontrivial even for fairly simple strategies.
6 Combining backpropagation and a zeroorder gradient estimates
We now present our algorithm for exploring deterministic policies in discrete action spaces, based on policies parameterized by a deep neural network. Our algorithm is inspired by finitedifference methods for stochastic gradientfree optimization [14, 21, 30] as well as exploration strategies in parameter space [26]. This algorithm can be viewed as a heuristic. We present it within the general MDP formulation of Section 4.1 for simplicity, although our experiments apply it to the greedy MDP of Section 4.2.
As described in Section 5.2, we consider the case where pairs (state, action) are embedded by a parametric function . The deterministic policy is parameterized by an additional vector , so that the action taken at state is defined as
The overall algorithm is described in Algorithm 1. In order to explore the policy space in a consistent manner during an episode, we uniformly sample a vector on the unit sphere and run the policy for the whole episode, where is a hyperparameter.
In addition to implementing a local random search in the policy space, the motivation for this randomization comes from stochastic gradientfree optimization [14, 21, 30, 9, 11], where the gradient of a differentiable function can be estimated with finite difference methods by
where the expectation is taken over the vector sampled on the unit sphere [21, chapter 9.3]. The constant will be absorbed by learning rates, so we ignore it in the following. Thus, given a (state, action) pair and the observed cumulative reward , we use as an estimator of the gradient of the expected cumulative reward with respect to (line (*) 1).
The motivation for the update of the network parameters is the following: given a function , we have and . Denoting by the termbyterm division of vectors (assuming contains only nonzero values) and the termbyterm multiplication operator, we obtain . The update (**) in the algorithm corresponds to taking in the above, and using as the estimated gradient of the cumulative reward with respect to , as before. Since we need to make sure that the ratios are bounded, in practice we use the sign of to avoid numerical issues. This “estimated” gradient is then backpropagated through the network. Preliminary experiments suggested that taking the sign was as effective as e.g., clipping, and was simpler since there is no parameter, so we use this heuristic in all our experiments.
The reasoning above is only a partial justification of the update rule (**) of Algorithm 1, because we neglected the dependency between the parameters and the operation that chooses the actions. Nonetheless, considering (**) as a crude approximation to some real estimator of the gradient seems to work very well in practice, as we shall see in our experiments. Finally, we use Adagrad [8] to update the parameters of the different layers. We found the use of Adagrad’s update scheme fairly important in practice, compared to other approaches such as RMSProp [42], even though RMSProp tended to work slightly better with Qlearning or REINFORCE in our experiments.
7 Experiments
7.1 Setup
We use Torch7^{3}^{3}3www.torch.ch for all our experiments. We connect our Torch code and models to StarCraft through a socket server. We ran experiments with deep Q networks (DQN) [19], policy gradient (PG) [46], and zero order (ZO). We did an extensive hyperparameters search, in particular over (for epsilongreedy exploration in DQN), (for policy gradient’s softmax), learning rates, optimization methods, RL algorithms variants, and potential annealings. See A.2 in Appendix for more details.
7.2 Baseline heuristics
As all the results that we report are against the builtin AI, we compare our win rates to the ones of (strong) baseline heuristics. Some of these heuristics often perform the micromanagement in fullfledged StarCraft bots [23], and are the basis of heuristic search [5]. The baselines are the following:

random no change (rand_nc): select a random target for each of our units and do not change this target before it dies (or our unit dies). This spreads damage over several enemy units, and can be rather bad when there are collisions (because it can require our units to move a lot to be in range of their target).

noop: literally send no action, that is something that is forbidden for our models to do. In this case, the builtin AI will control our units, so this exhibit the symmetry (or not!) of a given scenario. As we are always in a defensive position, with the enemy commanded to walk towards us, all other things considered equal (number of units), it should be easier for the defending builtin AI than for the attacking one.

closest (c): each of our units targets the enemy unit closest to it. This is not a bad heuristic as enemy units formation (because of collisions) will always make it so that several of our units have the same opponent unit as closest unit (some form of focus firing), but not all of them (no overkill). It is also quite robust for melee units (e.g. Zealots) as it means they spend less time moving and more time attacking.

weakest closest (wc): each of our units targets the weakest enemy unit. The distance of the enemy unit to the center of mass of our units is used for tiebreaking. This may overkill.

no overkill no change (nok_nc): same as the weakest closest heuristic, but register the number of our units that target each opponent unit, choosing another target to focus fire when it becomes overkill to keep targeting a given unit. Each of our units keep firing on their target without changing (that would lead to erratic behavior). Note that the “no overkill” component of the heuristic cannot easily take the dynamics of the game into account, and so if our units die without doing their expected damage on their target, “no overkill” can be detrimental (as it is implemented).
7.3 Results
The first thing that we looked at were sliding average win rates (over 400 battles) during training against the builtin AI of the various models. In Figure 1, we can see than DQN is much more dependent on initialization and variable (fickling) than zero order (ZO). DQN can unlearn, reach suboptimal plateaux, or overall need a lot of exploration to start learning (high sample complexity).
For all the results that we present in Tables 1 and 2, we ran the models in “test mode” by making them deterministic. For DQN we remove the epsilongreedy exploration (set ), for PG we do not sample in the Gibbs policy but instead take the valuemaximizing action, and for ZO we do not add noise to the last layer.
We can see in Table 1 that m15v16 is at the advantage of our player’s side (noop is at 81% win rate), whereas w15v17 is hard (c is at 20% win rate). By looking just at the results of the heuristics, we can see that overkill is a problem on m15v16 and w15v17 (nok_nc is better than wc). “Attack closest” (c) is approximatively as good as nok_nc at spreading damage, and thus better on m15v16 because there are lots of collisions (and attacking the closest unit is going to trigger less movements).
Overall, the zero order optimization outperforms both DQN and PG (REINFORCE) on most of the maps. The only map on which DQN and PG perform well is m5v5. It seems to be easier to learn a focus firing heuristic (e.g. “attack weakest”) by identifying and locking on a feature, than to also learn not to “overkill”.
heuristics  RL  
map  rand_nc  noop  c  wc  nok_nc  DQN  PG  ZO 
dragoons_zealots  .14  .49  .67  .83  .50  .61  .69  .90 
m5v5  .49  .84  .94  .96  .83  .99  .92  1. 
m15v16  .00  .81  .81  .10  .68  .13  .19  .79 
w15v17  .19  .10  .20  .02  .12  .16  .14  .49 

We then studied how well a model trained on one of the previous maps performs on maps with a different number of units, to test generalization. Table 2 contains the results for this experiment. We observe that DQN performs the best on m5v5 when trained on m15v16, because it learned a simpler (but more efficient on m5v5) heuristic. “Noop” and “attack closest” are quite good with the large Marines map because they generate less moves (and less collisions). Overall, ZO is consistently significantly better than other RL algorithms on these generalization tasks, even though it does not reach an optimal strategy.
train map  test map  best heuristic  DQN  PG  ZO 

m15v16  m5v5  .96 (wc/c)  .96  .79  .80 
m15v15  .97 (c)  .27  .16  .80  
m18v18  .98 (c/noop)  .18  .25  .82  
m18v20  .63 (noop)  .00  .01  .17  
w15v17  w5v5  .78 (c)  .70  .70  .74 
w15v13  1. (rand_nc/c)  1.  .99  1.  
w15v15  .95 (c)  .87  .61  .99  
w18v18  .99 (c)  .92  .56  1.  
w18v20  .71 (c)  .31  .24  .76 
7.4 Interpretation of the learned policies
We visually inspected the model’s performance on large battles. On the larger Marines map (m15v16), DQN learned to focus fire. Because this map has many units, focus firing leads to units bumping into each other to try to focus on a single unit. The PG player seemed to have a policy that attacks the closest marine, though it doesn’t do a good job switching targets. The Marines that are not in range often bump into each other. Our zero order optimization learns a hybrid between focus firing and attacking the closest unit. Units would switch to other units in range if possible, but still focus on specific targets. This leads to most Marines attacking constantly, as well as focus firing when they can. However, the learned strategy was not perfected, since Marines would still split their fire occasionally when left with few units.
In the Wraiths map (w15v17), the DQN player’s strategy was hard to decipher. The most likely explanation is that they tried to attack the closest target, though it is likely the algorithm did not converge to a specific strategy. The PG player learned to focus fire. However, because it only takes 6 Wraiths to kill another, 9 actions are "wasted" (at the beginning of the fight, when all our units are alive). Our zero order player learns that focusing only on one enemy is not good, but it does not learn how many attacks are necessary. This leads to a much higher win rate, but the player still assigns more than 6 Wraiths to an enemy target (maybe for robustness to the loss of one of our units), and occasionally will not focus fire when only a few Wraiths are remaining. This is similar to what the zero order player learned during the Marines scenario.
8 Conclusion
This paper presents two main contributions. First, it establishes StarCraft micromanagement scenarios as complex benchmarks for reinforcement learning: with durative actions, delayed rewards, and large action spaces making random exploration infeasible. Second, it introduces a new reinforcement learning algorithm that performs better than prior work (DQN, PG) for discrete action spaces in these micromanagement scenarios, with robust training (see Figure 1) and episodically consistent exploration (exploring in the policy space).
This work leaves several doors open and calls for future work. Simpler embedding models of state and actions, and variants of the model presented here, have been tried, none of which produced efficient units movement (e.g. taking a unit out of the fight when its hit points are low). There is ongoing work on convolutional networks based models that conserve the 2D geometry of the game (while embedding the discrete components of the state and actions). The zero order optimization technique presented here should be studied more in depth, and empirically evaluated on domains other than StarCraft (e.g. Atari). As for StarCraft scenarios specifically, the subsequent experiments will include selfplay (training and evaluation), multimap training (training more generic models), and more complex scenarios which include several types of advanced units with actions other than move and attack. Finally, the goal of playing full games of StarCraft should not get lost, so future scenarios would also include the actions of “recruiting” units (deciding which types of unit to use), as well as make use of them.
Acknowledgements
We thank YLan Boureau, Antoine Bordes, Florent Perronnin, Dave Churchill, Léon Bottou and Alexander Miller for helpful discussions and feedback about this work and earlier versions of the paper. We thank Timothée Lacroix and Alex Auvolat for technical contributions to our StarCraft/Torch bridge. We thank Davide Cavalca for his support on Windows virtual machines in our cluster environment.
References
 [1] Abel, D., Agarwal, A., Diaz, F., Krishnamurthy, A., and Schapire, R. E. Exploratory gradient boosting for reinforcement learning in complex domains. arXiv preprint arXiv:1603.04119 (2016).
 [2] Barto, A. G., Sutton, R. S., and Anderson, C. W. Neuronlike adaptive elements that can solve difficult learning control problems. IEEE transactions on systems, man, and cybernetics, 5 (1983), 834–846.
 [3] Bernstein, D. S., Givan, R., Immerman, N., and Zilberstein, S. The complexity of decentralized control of markov decision processes. Mathematics of operations research 27, 4 (2002), 819–840.
 [4] Busoniu, L., Babuska, R., and De Schutter, B. A comprehensive survey of multiagent reinforcement learning. IEEE Transactions on Systems, Man, And CyberneticsPart C: Applications and Reviews, 38 (2), 2008 (2008).
 [5] Churchill, D., Saffidine, A., and Buro, M. Fast heuristic search for rts game combat scenarios. In AIIDE (2012).
 [6] Clevert, D.A., Unterthiner, T., and Hochreiter, S. Fast and accurate deep network learning by exponential linear units (elus). arXiv preprint arXiv:1511.07289 (2015).
 [7] Deisenroth, M. P., Neumann, G., and Peters, J. A survey on policy search for robotics. Foundations and Trends in Robotics 2, 12 (2013), 1–142.
 [8] Duchi, J., Hazan, E., and Singer, Y. Adaptive subgradient methods for online learning and stochastic optimization. Journal of Machine Learning Research 12, Jul (2011), 2121–2159.
 [9] Duchi, J. C., Jordan, M. I., Wainwright, M. J., and Wibisono, A. Optimal rates for zeroorder convex optimization: the power of two function evaluations. arXiv preprint arXiv:1312.2139 (2013).
 [10] Gelly, S., and Wang, Y. Exploration exploitation in go: Uct for montecarlo go. In NIPS: Neural Information Processing Systems Conference Online trading of Exploration and Exploitation Workshop (2006).
 [11] Ghadimi, S., and Lan, G. Stochastic firstand zerothorder methods for nonconvex stochastic programming. SIAM Journal on Optimization 23, 4 (2013), 2341–2368.
 [12] Ghavamzadeh, M., Mahadevan, S., and Makar, R. Hierarchical multiagent reinforcement learning. Autonomous Agents and MultiAgent Systems 13, 2 (2006), 197–229.
 [13] Hu, J., and Wellman, M. P. Multiagent reinforcement learning: theoretical framework and an algorithm. In ICML (1998), vol. 98, pp. 242–250.
 [14] Kiefer, J., Wolfowitz, J., et al. Stochastic estimation of the maximum of a regression function. The Annals of Mathematical Statistics 23, 3 (1952), 462–466.
 [15] Littman, M. L. Markov games as a framework for multiagent reinforcement learning. In Proceedings of the eleventh international conference on machine learning (1994), vol. 157, pp. 157–163.
 [16] Liu, S., Louis, S. J., and Ballinger, C. Evolving effective micro behaviors in rts game. In Computational Intelligence and Games (CIG), 2014 IEEE Conference on (2014), IEEE, pp. 1–8.
 [17] Maes, F., Denoyer, L., and Gallinari, P. Structured prediction with reinforcement learning. Machine learning 77, 23 (2009), 271–301.
 [18] Mannor, S., Rubinstein, R. Y., and Gat, Y. The cross entropy method for fast policy search. In ICML (2003), pp. 512–519.
 [19] Mnih, V., Kavukcuoglu, K., Silver, D., Graves, A., Antonoglou, I., Wierstra, D., and Riedmiller, M. Playing atari with deep reinforcement learning. In Proceedings of NIPS (2013).
 [20] Mnih, V., Kavukcuoglu, K., Silver, D., Rusu, A. A., Veness, J., Bellemare, M. G., Graves, A., Riedmiller, M., Fidjeland, A. K., Ostrovski, G., et al. Humanlevel control through deep reinforcement learning. Nature 518, 7540 (2015), 529–533.
 [21] Nemirovsky, A.S., Yudin, D.B., and Dawson, E.R. Problem complexity and method efficiency in optimization.
 [22] Oh, J., Chockalingam, V., Singh, S., and Lee, H. Control of memory, active perception, and action in minecraft. arXiv preprint arXiv:1605.09128 (2016).
 [23] Ontanón, S., Synnaeve, G., Uriarte, A., Richoux, F., Churchill, D., and Preuss, M. A survey of realtime strategy game ai research and competition in starcraft. Computational Intelligence and AI in Games, IEEE Transactions on 5, 4 (2013), 293–311.
 [24] Osband, I., Blundell, C., Pritzel, A., and Van Roy, B. Deep exploration via bootstrapped dqn. arXiv preprint arXiv:1602.04621 (2016).
 [25] Osband, I., Roy, B. V., and Wen, Z. Generalization and exploration via randomized value functions. In Proceedings of The 33rd International Conference on Machine Learning (2016), pp. 2377–2386.
 [26] Rückstiess, T., Sehnke, F., Schaul, T., Wierstra, D., Sun, Y., and Schmidhuber, J. Exploring parameter space in reinforcement learning. Paladyn, Journal of Behavioral Robotics 1, 1 (2010), 14–24.
 [27] Sehnke, F., Osendorfer, C., Rückstieß, T., Graves, A., Peters, J., and Schmidhuber, J. Policy gradients with parameterbased exploration for control. In Artificial Neural NetworksICANN 2008. Springer, 2008, pp. 387–396.
 [28] Silver, D., Huang, A., Maddison, C. J., Guez, A., Sifre, L., Van Den Driessche, G., Schrittwieser, J., Antonoglou, I., Panneershelvam, V., Lanctot, M., et al. Mastering the game of go with deep neural networks and tree search. Nature 529, 7587 (2016), 484–489.
 [29] Silver, D., Lever, G., Heess, N., Degris, T., Wierstra, D., and Riedmiller, M. Deterministic policy gradient algorithms. In ICML (2014).
 [30] Spall, J. C. A onemeasurement form of simultaneous perturbation stochastic approximation. Automatica 33, 1 (1997), 109–112.
 [31] Stone, P., and Veloso, M. Teampartitioned, opaquetransition reinforcement learning. In Proceedings of the third annual conference on Autonomous Agents (1999), ACM, pp. 206–212.
 [32] Sukhbaatar, S., Szlam, A., and Fergus, R. Learning multiagent communication with backpropagation. arXiv preprint arXiv:1605.07736 (2016).
 [33] Sutton, R. S. Learning to predict by the methods of temporal differences. Machine learning 3, 1 (1988), 9–44.
 [34] Sutton, R. S., and Barto, A. G. Reinforcement learning: An introduction. MIT press, 1998.
 [35] Sutton, R. S., McAllester, D. A., Singh, S. P., Mansour, Y., et al. Policy gradient methods for reinforcement learning with function approximation. In NIPS (1999), vol. 99, pp. 1057–1063.
 [36] Synnaeve, G., and Bessiere, P. A bayesian model for rts units control applied to starcraft. In Computational Intelligence and Games (CIG), 2011 IEEE Conference on (2011), IEEE, pp. 190–196.
 [37] Szita, I., and Lörincz, A. Learning tetris using the noisy crossentropy method. Neural computation 18, 12 (2006), 2936–2941.
 [38] Tan, M. Multiagent reinforcement learning: Independent vs. cooperative agents. In Proceedings of the tenth international conference on machine learning (1993), pp. 330–337.
 [39] Tesauro, G. Temporal difference learning and tdgammon. Communications of the ACM 38, 3 (1995), 58–68.
 [40] Tesauro, G. Extending qlearning to general adaptive multiagent systems. In Advances in neural information processing systems (2003), p. None.
 [41] Thompson, W. R. On the likelihood that one unknown probability exceeds another in view of the evidence of two samples. Biometrika 25, 3/4 (1933), 285–294.
 [42] Tieleman, T., and Hinton, G. Lecture 6.5—RmsProp: Divide the gradient by a running average of its recent magnitude. COURSERA: Neural Networks for Machine Learning, 2012.
 [43] Van Hasselt, H., Guez, A., and Silver, D. Deep reinforcement learning with double qlearning. arXiv preprint arXiv:1509.06461 (2015).
 [44] Watkins, C. J., and Dayan, P. Qlearning. Machine learning 8, 34 (1992), 279–292.
 [45] Wender, S., and Watson, I. Applying reinforcement learning to small scale combat in the realtime strategy game starcraft: broodwar. In Computational Intelligence and Games (CIG), 2012 IEEE Conference on (2012), IEEE, pp. 402–408.
 [46] Williams, R. J. Simple statistical gradientfollowing algorithms for connectionist reinforcement learning. Machine learning 8, 34 (1992), 229–256.
Appendix A Appendix
a.1 StarCraft specifics
We advocate that using existing video games for RL experiments is interesting because the simulators are oftentimes complex, and we (the AI programmers) do not have control about the source code of the simulator. In RTS games like StarCraft, we do not have access to a simulator (and writing one would be a daunting task), so we cannot use (Monte Carlo) tree search [10] directly, even less so in the setting of full games [23]. In this paper, we consider the problem of micromanagement scenarios, a subset of full RTS play. Micromanagement is about making good use of a given set of units in an RTS game. Units have different features, like range, cooldown, hit points (health), attack power, move speed, collision box etc. These numerous features and the dynamics of the game advantage player that take the right actions at the right times. Specifically for the game(s) StarCraft, for which there are professional players, very good competitive players and professional players perform more than 300 actions per minute during intense battles.
We ran all our experiments on simple scenarios of battles of an RTS game: StarCraft: Broodwar. These scenarios can be considered small scale for StarCraft, but they already deem challenging for existing RL approaches. For an example scenario of 15 units (that we control) against 16 enemy units, even while reducing the action space to "atomic" actions (surrounding moves, and attacks), we obtain 24 (8+16) possible discrete actions per unit for our controller to choose from ( actions total) at the beginning of the battle. Battles last for tens of seconds, with durative actions, simultaneous moves, and at 24 frames per second. The strategies that we need to learn consist in coordinated sets of actions that may need to be repeated, e.g. focus firing without overkill. We use a featurization that gives access only to the state from the game, we do not preprocess the state to make it easier to learn a given strategy, thus keeping the problem elegant and unbiased.
For most of these tasks (“maps”), the number of units that our RL agent has to consider changes over an episode (a battle), as do its number of actions. The fact that we are playing in this specific adversarial environment is that if the units do not follow a coherent strategy for a sufficient amount of time, they will suffer an unrecoverable loss, and the game will be in a state of the game where the units will die very rapidly and make little damage, independently of how they play – a state that is mostly useless for learning.
Our tasks (“maps”) represent battles with homogeneous types of units, or with little diversity (2 types of unit for each of the players). For instance, they may use a unit of type Marine, that is one soldier with 40 hit points, an average move speed, an average range (approximately 10 times its collision size), 15 frames of cooldown, 6 of attack power of normal damage type (so a damage per second of 9.6 hit points per second, on a unit without armor).
On symmetric and/or monotyped maps, strategies that are required to win (on average) are “focus firing”, without overkill (not more units targeting a unit than what is needed to kill it). For perfect win rates, some maps may require that the AI moves its units out from the focus firing of the opponent.
a.2 Hyperparameters
Taking an action on every frame (24 times per second at the speed at which human play StarCraft) for every unit would spam the game needlessly, and it would actually prevent the units from moving^{4}^{4}4Because several actions are durative, including moves. Moves have a dynamic consisting of perunittype turn rate, max speed, and acceleration parameters.. We take actions for all units synchronously on the same frame, even skip_frames frames. We tried several values of this hyperparameter (5, 7, 9, 11, 13, 17) and we only saw smooth changes in performance. We ran all the following experiments with a skip_frames of 9 (meaning that we take about 2.6 actions per unit per second). We also report the strongest numbers for the baselines over all these skip frames. We optimize all the models after each battle (episode), with RMSProp (momentum or ), except for zeroorder for which we optimized with Adagrad (Adagrad did not seem to work better for DQN nor REINFORCE). In any case, the learning rate was chosen among .
For all methods, we tried experience replay, either with episodes (battles) as batches (of sizes 20, 50, 100), or additionally with random batches of quintuplets in the case of Qlearning, it did not seem to help compared to batching with the last battle. So, for consistency, we only present results where the training batches consisted of the last episode (battle).
For Qlearning (DQN), we tried two schemes of annealing for epsilon greedy, with the optimization batch, and , Both with , and respectively and . We found that the first works marginally better and used that in the subsequent experiments with and for most of the scenarios. We also used Double DQN as in [43] (thus implemented as target DQN). For the target/double network, we used a lag of 100 optimizations, thus a lag of 100 battles in all the following experiments. According to our initial runs/sweep, it seems to slightly help for some cases of overestimation of the Q value.
For REINFORCE we searched over .
For zeroorder, we tried .