Learning To Activate Relay Nodes: Deep Reinforcement Learning Approach
In this paper, we propose a distributed solution to design a multi-hop ad hoc network where mobile relay nodes strategically determine their wireless transmission ranges based on a deep reinforcement learning approach. We consider scenarios where only a limited networking infrastructure is available but a large number of wireless mobile relay nodes are deployed in building a multi-hop ad hoc network to deliver source data to the destination. A mobile relay node is considered as a decision-making agent that strategically determines its transmission range in a way that maximizes network throughput while minimizing the corresponding transmission power consumption. Each relay node collects information from its partial observations and learns its environment through a sequence of experiences. Hence, the proposed solution requires only a minimal amount of information from the system. We show that the actions that the relay nodes take from its policy are determined as to activate or inactivate its transmission, i.e., only necessary relay nodes are activated with the maximum transmit power, and nonessential nodes are deactivated to minimize power consumption. Using extensive experiments, we confirm that the proposed solution builds a network with higher network performance than current state-of-the-art solutions in terms of system goodput and connectivity ratio.
Given the rapid growth in mobile robotics, such as unmanned ground vehicles (UGVs) and unmanned aerial vehicles (UAVs), research on autonomous network formation for networked agent systems has gained much attention (Howard et al., 2002; Zavlanos & Pappas, 2008; Luo & Chen, 2012; Nazarzehi & Savkin, 2018). In the perspective of network design, the main goal is building an energy-efficient multi-hop network that can connect source nodes to terminal nodes via mobile relay nodes with energy constraints. Thus, the network topology is determined based on wireless connections between relay nodes. Possible applications include disaster networks (Yuan et al., 2016; Erdelj et al., 2017) and military networks (Van Hook et al., 2005) where only limited networking infrastructure is available, and mobile agents (e.g., robots) that are sparsely spread across a large area must act as relay nodes to deliver data in an ad hoc manner. In such a scenario, the mobility of the agents cannot be controlled centrally because of limitations in the networking infrastructure, which means the network cannot be designed by determining the location of the mobile relay nodes. Instead, the network must be designed by determining the wireless connections between mobile relay nodes roaming within preassigned areas. An example of such a network is shown in Figure 1(a).
However, designing an optimal network for relay nodes with mobility is challenging to do centrally because information about the real-time locations of the mobile nodes must be collected and considered for the optimal network topology. The problem becomes even more challenging when a large number of nodes need to be considered. Because the number of potential network topologies increases exponentially with the number of nodes, the computational complexity of finding the optimal topology becomes too high for a large-scale network to be practically deployed. Therefore, in this paper, we propose a distributed solution that is practically deployable because the mobile relay nodes make decisions about their own transmission ranges. Thus, the network topology is determined by the decisions that relay nodes make about themselves.
Unlike a centralized solution, where all necessary information can be made available to decision-making agents, each relay node in the proposed solution makes decisions based on only partial observations about the overall network. Thus, each relay node should be able to learn about the network from its own observations, with a minimum amount of information provided by the system. We adopt the deep reinforcement learning approach (Mnih et al., 2015; Silver et al., 2016; Van Hasselt et al., 2016) for sequential decisions, allowing each relay node to learn its environment (i.e., network) from a sequence of experiences. In the proposed decision-making framework, each relay node chooses the action that maximizes the estimated cumulative future rewards at its state. Specifically, each relay node makes a decision (i.e., action) of how much its transmission range needs to be increased or decreased based on its observations of the number of nodes in its current transmission range (i.e., state). The reward for the action is designed to consider both throughput improvement and the amount of additional transmission power (See Figure 1(b)). Note that the cumulative future reward should be available for all state-action pairs to find the optimal policy that returns the optimal action at each state. In a large-scale network with many nodes, however, the state space is too large to explore all state-action pairs and learn the rewards. Therefore, in this paper, we use a deep neural network with an input of state-action pairs and an output of estimated cumulative future reward and train it through a sequence of experiences.
Using an extensive set of experiments, we confirm that the proposed solution makes each relay node take actions to set its transmission range as either zero or maximum. Therefore, this can be viewed as the activeness of each node, i.e., an active node makes a connection with the maximum transmission range and an inactive node does not make a connection. Thus our autonomous activation system automatically selects the relay nodes needed to deliver data from the source to the destination and deactivates the transmission mode of unnecessary relay nodes to minimize power consumption.
The main contributions of this paper are summarized as follows.
We propose an autonomous network formation solution that can build a multi-hop ad hoc network in a distributed manner,
We formulate a decision-making process based on the Markov Decision Process (MDP) framework such that each relay node can determine its optimal wireless connections while explicitly considering the trade-off between overall network throughput and individual transmission power consumption,
We propose a learning process for the proposed solution such that individual relay nodes can make decisions using only minimal amount of information from the system,
We adopt a deep neural network to efficiently predict the cumulative future reward for large-scale state-actions pairs and learn the optimized policy by maximizing the estimated cumulative future reward, and
The proposed solution can activate only the few essential nodes needed to build a source-to-destination connection, leading to an autonomous activation system.
The rest of our paper is organized as follows. In Section 2, we briefly review related works. We introduce a wireless network model in Section 3. Section 4 provides the proposed distributed decision-making process and corresponding procedures for the system and nodes. An extensive set of experimental results is provided in Section 5. Finally, we draw conclusions in Section 6.
2 Related Works
Network formation strategy in wireless ad hoc networks has been studied in the context of self-organizing networks (Sohrabi et al., 2000; Kim & Chung, 2006). A protocol design for the self-organization of wireless sensor networks with a large number of static and highly energy constrained nodes is proposed in (Sohrabi et al., 2000). In (Kim & Chung, 2006), a self-organizing routing protocol for mobile sensor nodes is described. The proposed protocol declares membership in clusters as sensors move and confirms whether a mobile sensor node can communicate with a specific cluster head within a specific time slot. Even though those self-organizing protocols can provide solutions to network design, they require centralized planning, which necessitates a large amount of system overhead.
To overcome that limitation, distributed approaches in which network nodes can make their own decisions have been proposed. One widely adopted distributed decision-making approach is using game theory to consider how individual players choose their own actions when interacting with other players. In (Komali et al., 2008; Kwon & Park, 2017a), game-theoretic, distributed topology control for wireless transmission power is proposed for sensor networks. The purpose of topology control is to assign a per-node optimal transmission power such that the resulting topology can guarantee target network connectivity. The similar topology control game in (Eidenbenz et al., 2006) aims to choose the optimal power level for network nodes in an ad hoc network to ensure the desired connectivity properties. The dynamic topology control scheme presented in (Xu et al., 2016) prolongs the lifetime of a wireless sensor network based on a non-cooperative game. In (Kwon & Park, 2017b), a link formation game in a network coding-deployed network is proposed with low computational complexity to be used in a large-scale network.
Even though game-theoretic approaches can provide distributed solutions with theoretical analysis, the solutions often provide only mediocre performance in practical systems because they rely on strong assumptions of perfect information about other players (e.g., actions, payoff functions, strategies, etc.). However, information about the nodes in wireless mobile networks is often private and therefore not completely available to other nodes. Even when information is available, it is still difficult for all nodes to have perfect information in real-time. Therefore, each node should be able to learn its environment from partially available information of the network.
A node’s partial observations of its environment can be well-captured by the agent-environment interaction in the MDP framework and reinforcement learning (Le et al., ). For example, an MDP-based network formation strategy is proposed in (Kwon & Park, 2019) and shows that an intermediate node can satisfy the Markov property by deploying network coding. Then, policy-compliant intermediate nodes can find an optimal policy based on the value iteration, thereby adaptively evolving the network topology against network dynamics in a distributed manner. In (Hu & Fei, 2010; Bhorkar et al., 2012), Q-learning based distributed solutions for relay nodes are proposed. By updating the Q-values for state-action pairs, each node can learn how to act optimally by experiencing the consequences of its actions. For example, a Q-learning-based adaptive network formation protocol for energy-efficient underwater sensor networks is proposed in (Hu & Fei, 2010), and an opportunistic node-connecting strategy based on Q-learning in wireless ad hoc networks is discussed in (Bhorkar et al., 2012). A deep reinforcement learning-based solution is provided in (Valadarsky et al., 2017); it proposes a network connection strategy that lowers the congestion ratio based on deep reinforcement learning in wired networks, leading to a data-driven network formation scheme. An experimental study of a reinforcement learning-based design for multi-hop networks is described in (Syed et al., 2016), and more machine learning-based approaches are presented in the survey paper in (Boutaba et al., 2018).
Although those studies of machine learning techniques have broadened the research agenda, some still resort to impractical scenarios requiring infeasible information (e.g., the state transition probability of each agent), and others do not consider the resource-limited characteristics of the agents in wireless mobile networks (e.g., battery powered device). Therefore, in this paper, we propose an energy-efficient solution based on a deep Q-network that does not require knowledge of the state transition probability.
3 Autonomous Nodes with Adjustable Wireless Transmission Range
We model a wireless mobile ad hoc network as a directed graph that consists of a set of nodes and a set of directed links at time step . There are three types of nodes in the network, which are source, relay and terminal, and the node can be one of those types. A source node is denoted by where is an index set of source nodes. Similarly, the index set of terminals for the source node is denoted as .
In this paper, we consider the most generalized network scenario, where multiple source nodes simultaneously transmit data toward their own terminal nodes, and each source node has an independent set of terminal nodes. Specifically, the source node for aims to deliver its data to multiple terminal nodes for all . Therefore, flows should be simultaneously considered, where denotes the size of a set. The total index set of all terminals in is denoted as , and the numbers of source nodes and terminal nodes are denoted by and , respectively.
A relay node for , where denotes an index set of relay nodes, can receive data from nodes and forward it to other nodes. Thus, relay nodes play an essential role whenever a source node is unable to directly transmit data to its terminal nodes. We consider the relay nodes to be wireless mobile devices that can move around within a bounded region with power constraints. Moreover, each relay node can adaptively decide its transmission range by adjusting its transmission power, which determines the range of potential delivery of its data. We denote the radius of the transmission range of as , and the Euclidean distance between node and node at time step is . Then, is located in the transmission range of if , and can receive data from . The radius of the transmission range of is bounded by its largest transmission range as determined by the energy constraint, i.e., .
The deployment of relay nodes naturally leads to a multi-hop ad hoc network, and thus the network performance (e.g., throughput, connectivity and energy consumption) depends highly on the data path in delivery. Because each relay node is an autonomous agent that can independently and strategically decide its transmission range, the data path in delivery is determined by the decisions of the nodes. In the next section, we propose a deep reinforcement learning-based decision-making process that allows each node to make the optimal decision.
4 Distributed Decision-making for Autonomous Nodes
In this section, we propose a sequential decision-making solution that determines the transmission range of relay nodes.
4.1 Proposed Solution for the Decision-making Process
Each relay node strategically and repeatedly decides its transmission range by considering the reward for each selected action, where the reward represents the improvement of network throughput at the cost of the power required to take the action. The proposed decision-making model is formulated by an MDP, expressed as a tuple , where is a finite state space, is a finite action space, is a reward, and is a discount factor.
A state of node represents the number of nodes located in its transmission range at time step , which implies the number of nodes that can relay data from other nodes. Because each node is always located within its own transmission range, the size of a state is at least and at most , i.e., .
An action of node represents the difference between the radius of the transmission range at time step and , i.e.,
If (i.e., ), the node increases the transmission range. Similarly, if , the node decreases the transmission range (i.e., ). The node can maintain the same transmission range by taking action . If the radius of the current transmission range is zero (i.e., ), the negative action (i.e., ) does not change . Similarly, if a node is already set at its maximum transmission range (i.e., ), the positive action (i.e., ) does not change .
The reward of node at time step is defined as a quasi-linear function that consists of the throughput improvement and the amount of transmission power consumption additionally required, expressed as
In (2), is a constant that guarantees the reward to be non-negative, and denotes the network throughput of . Thus, is the throughput improvement at the cost of taking action . The cost for the action intrinsically includes the amount of additional transmit power consumption at the node, as well as the penalty for causing additional inter-node interference in the network. Note that the throughput improvement (i.e., ) is a network-dependent variable that is identical for all relay nodes included in the same network. On the other hand, the cost for additional power consumption (i.e., ) is node-dependent. The weight can be used to balance the throughput improvement and additional power consumption. For example, if the goal is only to improve the throughput without the consideration of power consumption associated with taking action, can be set. On the other hand, if , the throughput improvement is not taken into account in the reward, i.e., the network throughput is not interesting to the node. The scaler can balance the range of and .
As a solution to the proposed MDP problem, we adopt deep reinforcement learning. Each node interacts with the system through a sequence of state observations, actions, and rewards. The goal of the node is to select actions in a fashion that maximizes its cumulative future reward. To estimate that cumulative future reward, we define the Q-function of node as,
which is the expected cumulative sum of reward discounted by at each time step , achievable by a behavior policy after making an observation and taking an action at the time step . denotes the expected value when the policy is used, where the policy maps a state of the node to an action such that . is the horizon of a finite MDP.
Because we consider a large-scale network that includes many wireless nodes and induces a large state space in the MDP framework, we use a Double Deep Q-Network (DDQN; (Van Hasselt et al., 2016)) to optimize the Q-function. The DDQN includes an online network and a target network. The parameters of the online network in the DDQN of node at time step , denoted as , are trained to minimize the loss function defined in (4).
Here, represents the parameter of the target network, which is updated every steps, where is the update interval for the target network. The DDQN evaluates the policy according to the online network, and uses the target network to compute the target Q-value.
The optimal policy is defined to maximize the Q-function and it returns the optimal action for a given state , i.e.,
In this system, the -greedy policy is used such that the node chooses the action that follows the obtained policy with a probability of , and it chooses an action uniformly at random, otherwise.
In the next section, we describe procedures how the proposed decision-making solution can be adopted in our autonomous node activation system.
4.2 Procedures of the Proposed System
The proposed system includes an online learning algorithm for the relay nodes so that they learn their own policy in real time.
Each node owns a DDQN to build its own policy. Specifically, all nodes determine their transmission range at every time step, and this forms the network topology at time . Then, the network throughput measured from the network topology is broadcast to all relay nodes. Except for the network throughput , which is shared with all nodes, all the other parameters used in procedures such as , , , , are local, i.e., they are used only at node and not shared with other nodes. In this way, the role of the system controller is minimized in the proposed system; all the individual nodes participate actively in the proposed system, which leads to a decentralized solution.
The overall flow of the procedures performed by individual nodes in the proposed system is shown in Figure 2. The detailed description of the procedures is provided in Procedure 1 in conjunction with the subfunctions described in Procedure 2 and Procedure 3.
Procedure 1 describes how individual nodes determine their actions and update their policies at every time step. In the initialization stage, each node sets up its initial transmission range and DDQN. Then, each node chooses an action determined by the function described in Procedure 2 and adjusts its transmission range. All the network nodes transmit data simultaneously, and the network throughput is evaluated. Finally, each node updates its state and DDQN based on Procedure 3. These procedures, i.e., get the action, update transmission range, transmit data, evaluate network throughput, and update state and DDQN, are repeated until the delivery is terminated.
Procedure 2 describes the process for getting actions from the DDQN. For an -greedy policy, a number is randomly chosen from a uniform distribution in the range of . If , the node explores a new action by randomly selecting an action from the action set. Otherwise, the node exploits the trained policy by selecting the action that maximizes .
Procedure 3 describes how to train the DDQN. The node calculates the reward based on (2) and finds the parameter that minimizes the loss function in (4). The parameter is updated using the gradient descent method with a learning rate of . The target network is updated every time steps to stabilize the training.
In the next section, we deploy the proposed procedures in a Wi-Fi Direct network and evaluate the performance.
In these experiments, we consider a wireless mobile ad hoc network where multiple relay nodes bridge source nodes and terminal nodes. All relay nodes are policy-compliant agents, i.e., each node simply takes the actions dictated by its policy. Hence, each node works to build an optimal policy by training its DDQN from a sequence of experiences.
5.1 Experiment Setup
|PHY Data Rate||1300|
The considered wireless network consists of two source nodes, two terminals and multiple mobile relay nodes. The mobile relay nodes are connected by Wi-Fi Direct with IEEE 802.11ac standard MCS-9. The transmit power is computed based on a path loss model, expressed as
where , , , and denote the transmit power, receive power, wave length, and distance between the transmitter and receiver, respectively. The parameters used in this experiment are specified by the IEEE 802.11ac standard (IEE, 2013; cis, 2014) and shown in Table 1.
The network size is the area of the bounded region in which the mobile nodes are allowed to move, and the number of relay nodes located in the bounded region is determined by the Poisson Point Process (PPP) with a node density of , which reflects the characteristics of mobile networks. Moreover, the locations of relay nodes are randomly distributed over the bounded region, which captures their mobility. In this paper, we define an episode as a set of time steps with the same network members. Hence, the number of relay nodes is reset whenever a new episode starts, and the location of the nodes changes in every time step.
Figure 3 shows the number of nodes in networks with different network sizes. The line in the middle of each box denotes the median of the experimental results, where on average , , , and nodes are located in networks for the size of , , , , and , respectively. The top and bottom lines of each box represent the th and th percentiles, respectively.
The action set has elements, with each element in the range of with a step size of . The maximum radius of the transmission range is set to . The parameters for the reward function defined in (2) are set as , and . The discount factor is set to . The neural network used in the DDQN has two fully connected layers, with a hidden layer size of and ReLU nonlinearities. The neural network is optimized using the RMSProp optimizer with a learning rate of . The target network update interval is set to . For learning stability, we rescaled the input of the DDQN and the value of the reward by dividing by and , respectively. The greedy rate decays linearly from to in steps.
The network performance is evaluated based on the system goodput (Miao et al., 2016), defined as the sum of data rates successfully delivered to terminal nodes, i.e.,
where denotes data generated at a source node , () denotes a set of terminal nodes that successfully receive , represents the size of data set , and denotes the travel time for data set to arrive at terminal node . The connectivity ratio is defined as the number of successfully connected flows out of all flows from sources to terminals.
5.2 Experimental Results
The three network performance measures, connectivity ratio, system goodput and power consumption per node, are evaluated over time for networks with four different sizes. Figure 4 presents the average results from independent episodes and Table 2 shows the average results in the range of time steps (i.e., after is decayed to ).
As shown by the results in Figure 3(a) and Figure 3(c), the network size does not significantly affect the connectivity ratio or energy consumption per node. Thus the proposed system is resilient against network size, and can therefore be a scalable solution for network formation. The advantage of scalability comes from the characteristics of a distributed solution in which individual nodes need not consider the size of the network. Instead, each node considers only its own actions and feedback from the network. Thus, the effects of network size on the decision-making of each node are significantly limited. On the other hand, the system goodput decreases as the network size increases, as shown in Figure 3(b), because the number of hops that the data traverse to reach a terminal increases, as the network size increases.
The network performance achieved by the proposed solution can be understood by investigating how the transmission range of individual nodes, as well as the resulting network, are by the learning process over time.
In Figure 5, the radius of the transmission range is visualized for nodes over time steps.
The learning process begins at time step by initializing the transmission range of all nodes as zero. Then, nodes gradually increase their transmission ranges to make stable connections from sources to terminals in the early stage of the learning process (e.g., between and time steps). This is because the reward function defined in (2) is designed such that the throughput enhancement (i.e., ) is high enough at this stage to take the action that enlarges the transmission range. The corresponding changes in the radius of the transmission range between and steps are shown in Figure 5, and the actual connections are depicted in Figure 5(a) and Figure 5(b).
As more learning stages are processed, the changes in the transmission range of each node gradually slow down, and the transmission range of each node eventually converges to either zero or the maximum (i.e., ), as shown at time step . This can be viewed as the activeness of each node, i.e., an active node makes a connection with the maximum transmission range, and an inactive node does not make a connection. Note that the node activeness is determined to improve the network throughput as can be seen by comparing Figure 5(c) and Figure 5(d). Nodes change their transmission range to find a shorter path from sources to terminals. Thus, the proposed solution determines which relay nodes are essential for network throughput improvement and simultaneously minimizes power consumption by turning off potentially unnecessary relay nodes.
5.3 Performance Comparison
We next compare the performance of the proposed solution with three existing solutions.
Value Iteration (Kwon & Park, 2019): A state-of-the-art model-based MDP solution with the knowledge of state transition probability and reward. This solution gives an analytical solution to the near-optimal policy. Then, the state transition matrix can be found using that policy, which allows the system to analytically determine a stationary network. In this experiment, the optimality level of the policy is set to .
TCLE (Xu et al., 2016): A state-of-the-art distributed solution for designing node connections. This solution enables a node to choose its transmission power by considering the target algebraic connectivity (Gross & Yellen, 2004) against transmission energy dissipation. In this experiment, the target algebraic connectivity is set to .
Random Selection: This solution enables a node to randomly select its action from a given action set. In this experiment, random selection used the setting of .
|System Goodput ||461.08||427.15||328.51||240.79|
|System Goodput ||323.05||268.00||202.93||191.83|
Table 3 shows the system goodput and connectivity ratio of the four distributed solutions with two network sizes. At both sizes, the proposed solution achieves higher system goodput than value iteration while maintaining a comparable connectivity ratio. Note that the value iteration method requires much more information than the proposed solution; the state transition probability cannot be easily obtained in real-world applications. Thus, the proposed solution is more practical than value iteration. The random selection method shows a lower performance than both the proposed solution and value iteration because it does not include a learning process. The TCLE method shows the worst performance for both system goodput and connectivity ratio because actions are taken without considering specific source-to-terminal connections. TCLE considers only general network connectivity in terms of algebraic connectivity.
In this paper, we have proposed a distributed solution based on the DDQN, which enables relay nodes to make decisions for multi-hop ad hoc network formation with only partial observations in a network with many mobile relay nodes. The proposed solution can activate essential relay nodes and deactivate unnecessary relay nodes, leading to an autonomous node activation system that can successfully build a network in a distributed manner. A deep reinforcement learning algorithm is deployed for decision-making at the relay nodes, which update their wireless transmission ranges by observing the number of nodes in their current transmission ranges. The reward function includes network throughput and transmission power consumption so that each relay node can choose its action by explicitly considering the trade-off between network performance and its own power consumption. The DDQN used in the decision-making process can efficiently optimize the Q-function. Our experimental results confirm that the network built by the proposed system outperforms those built by existing state-of-the-art solutions in terms of system goodput and connectivity ratio.
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