We propose a general framework for entropy-regularized average-reward reinforcement learning in Markov decision processes (MDPs). Our approach is based on extending the linear-programming formulation of policy optimization in MDPs to accommodate convex regularization functions. Our key result is showing that using the conditional entropy of the joint state-action distributions as regularization yields a dual optimization problem closely resembling the Bellman optimality equations. This result enables us to formalize a number of state-of-the-art entropy-regularized reinforcement learning algorithms as approximate variants of Mirror Descent or Dual Averaging, and thus to argue about the convergence properties of these methods. In particular, we show that the exact version of the TRPO algorithm of Schulman et al. (2015) actually converges to the optimal policy, while the entropy-regularized policy gradient methods of Mnih et al. (2016) may fail to converge to a fixed point. Finally, we illustrate empirically the effects of using various regularization techniques on learning performance in a simple reinforcement learning setup.

International audienceWe consider online learning in finite stochastic Markovian environments where in each time step a new reward function is chosen by an oblivious adversary. The goal of the learning agent is to compete with the best stationary policy in hindsight in terms of the total reward received. Specifically, in each time step the agent observes the current state and the reward associated with the last transition, however, the agent does not observe the rewards associated with other state-action pairs. The agent is assumed to know the transition probabilities. The state of the art result for this setting is an algorithm with an expected regret of O(T^2/3 ln T). In this paper, assuming that stationary policies mix uniformly fast, we show that after T time steps, the expected regret of this algorithm (more precisely, a slightly modified version thereof) is O(T^1/2 ln T), giving the first rigorously proven, essentially tight regret bound for the problem

Next-generation wireless deployments are characterized by being dense and uncoordinated, which often leads to inefficient use of resources and poor performance. To solve this, we envision the utilization of completely decentralized mechanisms to enable Spatial Reuse (SR). In particular, we focus on dynamic channel selection and Transmission Power Control (TPC). We rely on Reinforcement Learning (RL), and more specifically on Multi-Armed Bandits (MABs), to allow networks to learn their best configuration. In this work, we study the exploration-exploitation trade-off by means of the ε-greedy, EXP3, UCB and Thompson sampling action-selection, and compare their performance. In addition, we study the implications of selecting actions simultaneously in an adversarial setting (i.e., concurrently), and compare it with a sequential approach. Our results show that optimal proportional fairness can be achieved, even when no information about neighboring networks is available to the learners and Wireless Networks (WNs) operate selfishly. However, there is high temporal variability in the throughput experienced by the individual networks, especially for ε-greedy and EXP3. These strategies, contrary to UCB and Thompson sampling, base their operation on the absolute experienced reward, rather than on its distribution. We identify the cause of this variability to be the adversarial setting of our setup in which the set of most played actions provide intermittent good/poor performance depending on the neighboring decisions. We also show that learning sequentially, even if using a selfish strategy, contributes to minimize this variability. The sequential approach is therefore shown to effectively deal with the challenges posed by the adversarial settings that are typically found in decentralized WNs.

Spatial Reuse (SR) has recently gained attention to maximize the performance of IEEE 802.11 Wireless Local Area Networks (WLANs). Decentralized mechanisms are expected to be key in the development of SR solutions for next-generation WLANs, since many deployments are characterized by being uncoordinated by nature. However, the potential of decentralized mechanisms is limited by the significant lack of knowledge with respect to the overall wireless environment. To shed some light on this subject, we show the main considerations and possibilities of applying online learning to address the SR problem in uncoordinated WLANs. In particular, we provide a solution based on Multi-Armed Bandits (MABs) whereby independent WLANs dynamically adjust their frequency channel, transmit power and sensitivity threshold. To that purpose, we provide two different strategies, which refer to selfish and environment-aware learning. While the former stands for pure individual behavior, the second one considers the performance experienced by surrounding networks, thus taking into account the impact of individual actions on the environment. Through these two strategies we delve into practical issues of applying MABs in wireless networks, such as convergence guarantees or adversarial effects. Our simulation results illustrate the potential of the proposed solutions for enabling SR in future WLANs. We show that substantial improvements on network performance can be achieved regarding throughput and fairness.