CrossNorm: Normalization for Off-Policy TD Reinforcement Learning

Off-policy temporal difference (TD) methods are a powerful class of reinforcement learning (RL) algorithms. Intriguingly, deep off-policy TD algorithms are not commonly used in combination with feature normalization techniques, despite positive effects of normalization in other domains. We show that naive application of existing normalization techniques is indeed not effective, but that well-designed normalization improves optimization stability and removes the necessity of target networks. In particular, we introduce a normalization based on a mixture of on- and off-policy transitions, which we call cross-normalization. It can be regarded as an extension of batch normalization that re-centers data for two different distributions, as present in off-policy learning. Applied to DDPG and TD3, cross-normalization improves over the state of the art across a range of MuJoCo benchmark tasks

From Weak Learning to Strong Learning in Fictitious Play Type Algorithms

The paper studies the highly prototypical Fictitious Play (FP) algorithm, as well as a broad class of learning processes based on best-response dynamics, that we refer to as FP-type algorithms. A well-known shortcoming of FP is that, while players may learn an equilibrium strategy in some abstract sense, there are no guarantees that the period-by-period strategies generated by the algorithm actually converge to equilibrium themselves. This issue is fundamentally related to the discontinuous nature of the best response correspondence and is inherited by many FP-type algorithms. Not only does it cause problems in the interpretation of such algorithms as a mechanism for economic and social learning, but it also greatly diminishes the practical value of these algorithms for use in distributed control. We refer to forms of learning in which players learn equilibria in some abstract sense only (to be defined more precisely in the paper) as weak learning, and we refer to forms of learning where players' period-by-period strategies converge to equilibrium as strong learning. An approach is presented for modifying an FP-type algorithm that achieves weak learning in order to construct a variant that achieves strong learning. Theoretical convergence results are proved.Comment: 22 page

Addressing Function Approximation Error in Actor-Critic Methods

In value-based reinforcement learning methods such as deep Q-learning, function approximation errors are known to lead to overestimated value estimates and suboptimal policies. We show that this problem persists in an actor-critic setting and propose novel mechanisms to minimize its effects on both the actor and the critic. Our algorithm builds on Double Q-learning, by taking the minimum value between a pair of critics to limit overestimation. We draw the connection between target networks and overestimation bias, and suggest delaying policy updates to reduce per-update error and further improve performance. We evaluate our method on the suite of OpenAI gym tasks, outperforming the state of the art in every environment tested.Comment: Accepted at ICML 201

Two Timescale Convergent Q-learning for Sleep--Scheduling in Wireless Sensor Networks

In this paper, we consider an intrusion detection application for Wireless Sensor Networks (WSNs). We study the problem of scheduling the sleep times of the individual sensors to maximize the network lifetime while keeping the tracking error to a minimum. We formulate this problem as a partially-observable Markov decision process (POMDP) with continuous state-action spaces, in a manner similar to (Fuemmeler and Veeravalli [2008]). However, unlike their formulation, we consider infinite horizon discounted and average cost objectives as performance criteria. For each criterion, we propose a convergent on-policy Q-learning algorithm that operates on two timescales, while employing function approximation to handle the curse of dimensionality associated with the underlying POMDP. Our proposed algorithm incorporates a policy gradient update using a one-simulation simultaneous perturbation stochastic approximation (SPSA) estimate on the faster timescale, while the Q-value parameter (arising from a linear function approximation for the Q-values) is updated in an on-policy temporal difference (TD) algorithm-like fashion on the slower timescale. The feature selection scheme employed in each of our algorithms manages the energy and tracking components in a manner that assists the search for the optimal sleep-scheduling policy. For the sake of comparison, in both discounted and average settings, we also develop a function approximation analogue of the Q-learning algorithm. This algorithm, unlike the two-timescale variant, does not possess theoretical convergence guarantees. Finally, we also adapt our algorithms to include a stochastic iterative estimation scheme for the intruder's mobility model. Our simulation results on a 2-dimensional network setting suggest that our algorithms result in better tracking accuracy at the cost of only a few additional sensors, in comparison to a recent prior work