Q-Learning for Continuous State and Action MDPs under Average Cost Criteria

For infinite-horizon average-cost criterion problems, we present several approximation and reinforcement learning results for Markov Decision Processes with standard Borel spaces. Toward this end, (i) we first provide a discretization based approximation method for fully observed Markov Decision Processes (MDPs) with continuous spaces under average cost criteria, and we provide error bounds for the approximations when the dynamics are only weakly continuous under certain ergodicity assumptions. In particular, we relax the total variation condition given in prior work to weak continuity as well as Wasserstein continuity conditions. (ii) We provide synchronous and asynchronous Q-learning algorithms for continuous spaces via quantization, and establish their convergence. (iii) We show that the convergence is to the optimal Q values of the finite approximate models constructed via quantization. Our Q-learning convergence results and their convergence to near optimality are new for continuous spaces, and the proof method is new even for finite spaces, to our knowledge.Comment: 3 figure

Risk-Sensitive Reinforcement Learning: A Constrained Optimization Viewpoint

The classic objective in a reinforcement learning (RL) problem is to find a policy that minimizes, in expectation, a long-run objective such as the infinite-horizon discounted or long-run average cost. In many practical applications, optimizing the expected value alone is not sufficient, and it may be necessary to include a risk measure in the optimization process, either as the objective or as a constraint. Various risk measures have been proposed in the literature, e.g., mean-variance tradeoff, exponential utility, the percentile performance, value at risk, conditional value at risk, prospect theory and its later enhancement, cumulative prospect theory. In this article, we focus on the combination of risk criteria and reinforcement learning in a constrained optimization framework, i.e., a setting where the goal to find a policy that optimizes the usual objective of infinite-horizon discounted/average cost, while ensuring that an explicit risk constraint is satisfied. We introduce the risk-constrained RL framework, cover popular risk measures based on variance, conditional value-at-risk and cumulative prospect theory, and present a template for a risk-sensitive RL algorithm. We survey some of our recent work on this topic, covering problems encompassing discounted cost, average cost, and stochastic shortest path settings, together with the aforementioned risk measures in a constrained framework. This non-exhaustive survey is aimed at giving a flavor of the challenges involved in solving a risk-sensitive RL problem, and outlining some potential future research directions

Deep Reinforcement Learning for Wireless Sensor Scheduling in Cyber-Physical Systems

In many Cyber-Physical Systems, we encounter the problem of remote state estimation of geographically distributed and remote physical processes. This paper studies the scheduling of sensor transmissions to estimate the states of multiple remote, dynamic processes. Information from the different sensors have to be transmitted to a central gateway over a wireless network for monitoring purposes, where typically fewer wireless channels are available than there are processes to be monitored. For effective estimation at the gateway, the sensors need to be scheduled appropriately, i.e., at each time instant one needs to decide which sensors have network access and which ones do not. To address this scheduling problem, we formulate an associated Markov decision process (MDP). This MDP is then solved using a Deep Q-Network, a recent deep reinforcement learning algorithm that is at once scalable and model-free. We compare our scheduling algorithm to popular scheduling algorithms such as round-robin and reduced-waiting-time, among others. Our algorithm is shown to significantly outperform these algorithms for many example scenarios

Understanding Model-Based Reinforcement Learning and its Application in Safe Reinforcement Learning

Model-based reinforcement learning algorithms have been shown to achieve successful results on various continuous control benchmarks, but the understanding of model-based methods is limited. We try to interpret how model-based method works through novel experiments on state-of-the-art algorithms with an emphasis on the model learning part. We evaluate the role of the model learning in policy optimization and propose methods to learn a more accurate model. With a better understanding of model-based reinforcement learning, we then apply model-based methods to solve safe reinforcement learning (RL) problems with near-zero violation of hard constraints throughout training. Drawing an analogy with how humans and animals learn to perform safe actions, we break down the safe RL problem into three stages. First, we train agents in a constraint-free environment to learn a performant policy for reaching high rewards, and simultaneously learn a model of the dynamics. Second, we use model-based methods to plan safe actions and train a safeguarding policy from these actions through imitation. Finally, we propose a factored framework to train an overall policy that mixes the performant policy and the safeguarding policy. This three-step curriculum ensures near-zero violation of safety constraints at all times. As an advantage of model-based method, the sample complexity required at the second and third steps of the process is significantly lower than model-free methods and can enable online safe learning. We demonstrate the effectiveness of our methods in various continuous control problems and analyze the advantages over state-of-the-art approaches