Proximal Reinforcement Learning: A New Theory of Sequential Decision Making in Primal-Dual Spaces

In this paper, we set forth a new vision of reinforcement learning developed by us over the past few years, one that yields mathematically rigorous solutions to longstanding important questions that have remained unresolved: (i) how to design reliable, convergent, and robust reinforcement learning algorithms (ii) how to guarantee that reinforcement learning satisfies pre-specified "safety" guarantees, and remains in a stable region of the parameter space (iii) how to design "off-policy" temporal difference learning algorithms in a reliable and stable manner, and finally (iv) how to integrate the study of reinforcement learning into the rich theory of stochastic optimization. In this paper, we provide detailed answers to all these questions using the powerful framework of proximal operators. The key idea that emerges is the use of primal dual spaces connected through the use of a Legendre transform. This allows temporal difference updates to occur in dual spaces, allowing a variety of important technical advantages. The Legendre transform elegantly generalizes past algorithms for solving reinforcement learning problems, such as natural gradient methods, which we show relate closely to the previously unconnected framework of mirror descent methods. Equally importantly, proximal operator theory enables the systematic development of operator splitting methods that show how to safely and reliably decompose complex products of gradients that occur in recent variants of gradient-based temporal difference learning. This key technical innovation makes it possible to finally design "true" stochastic gradient methods for reinforcement learning. Finally, Legendre transforms enable a variety of other benefits, including modeling sparsity and domain geometry. Our work builds extensively on recent work on the convergence of saddle-point algorithms, and on the theory of monotone operators.Comment: 121 page

Boosting the Actor with Dual Critic

This paper proposes a new actor-critic-style algorithm called Dual Actor-Critic or Dual-AC. It is derived in a principled way from the Lagrangian dual form of the Bellman optimality equation, which can be viewed as a two-player game between the actor and a critic-like function, which is named as dual critic. Compared to its actor-critic relatives, Dual-AC has the desired property that the actor and dual critic are updated cooperatively to optimize the same objective function, providing a more transparent way for learning the critic that is directly related to the objective function of the actor. We then provide a concrete algorithm that can effectively solve the minimax optimization problem, using techniques of multi-step bootstrapping, path regularization, and stochastic dual ascent algorithm. We demonstrate that the proposed algorithm achieves the state-of-the-art performances across several benchmarks.Comment: 21 pages, 9 figure

An Actor-Critic Contextual Bandit Algorithm for Personalized Mobile Health Interventions

Increasing technological sophistication and widespread use of smartphones and wearable devices provide opportunities for innovative and highly personalized health interventions. A Just-In-Time Adaptive Intervention (JITAI) uses real-time data collection and communication capabilities of modern mobile devices to deliver interventions in real-time that are adapted to the in-the-moment needs of the user. The lack of methodological guidance in constructing data-based JITAIs remains a hurdle in advancing JITAI research despite the increasing popularity of JITAIs among clinical scientists. In this article, we make a first attempt to bridge this methodological gap by formulating the task of tailoring interventions in real-time as a contextual bandit problem. Interpretability requirements in the domain of mobile health lead us to formulate the problem differently from existing formulations intended for web applications such as ad or news article placement. Under the assumption of linear reward function, we choose the reward function (the "critic") parameterization separately from a lower dimensional parameterization of stochastic policies (the "actor"). We provide an online actor-critic algorithm that guides the construction and refinement of a JITAI. Asymptotic properties of the actor-critic algorithm are developed and backed up by numerical experiments. Additional numerical experiments are conducted to test the robustness of the algorithm when idealized assumptions used in the analysis of contextual bandit algorithm are breached

Bridging the Gap Between Value and Policy Based Reinforcement Learning

We establish a new connection between value and policy based reinforcement learning (RL) based on a relationship between softmax temporal value consistency and policy optimality under entropy regularization. Specifically, we show that softmax consistent action values correspond to optimal entropy regularized policy probabilities along any action sequence, regardless of provenance. From this observation, we develop a new RL algorithm, Path Consistency Learning (PCL), that minimizes a notion of soft consistency error along multi-step action sequences extracted from both on- and off-policy traces. We examine the behavior of PCL in different scenarios and show that PCL can be interpreted as generalizing both actor-critic and Q-learning algorithms. We subsequently deepen the relationship by showing how a single model can be used to represent both a policy and the corresponding softmax state values, eliminating the need for a separate critic. The experimental evaluation demonstrates that PCL significantly outperforms strong actor-critic and Q-learning baselines across several benchmarks.Comment: NIPS 201

Continuous-Time Mean-Variance Portfolio Selection: A Reinforcement Learning Framework

We approach the continuous-time mean-variance (MV) portfolio selection with reinforcement learning (RL). The problem is to achieve the best tradeoff between exploration and exploitation, and is formulated as an entropy-regularized, relaxed stochastic control problem. We prove that the optimal feedback policy for this problem must be Gaussian, with time-decaying variance. We then establish connections between the entropy-regularized MV and the classical MV, including the solvability equivalence and the convergence as exploration weighting parameter decays to zero. Finally, we prove a policy improvement theorem, based on which we devise an implementable RL algorithm. We find that our algorithm outperforms both an adaptive control based method and a deep neural networks based algorithm by a large margin in our simulations.Comment: 39 pages, 5 figure

Two-stage Deep Reinforcement Learning for Inverter-based Volt-VAR Control in Active Distribution Networks

Model-based Vol/VAR optimization method is widely used to eliminate voltage violations and reduce network losses. However, the parameters of active distribution networks(ADNs) are not onsite identified, so significant errors may be involved in the model and make the model-based method infeasible. To cope with this critical issue, we propose a novel two-stage deep reinforcement learning (DRL) method to improve the voltage profile by regulating inverter-based energy resources, which consists of offline stage and online stage. In the offline stage, a highly efficient adversarial reinforcement learning algorithm is developed to train an offline agent robust to the model mismatch. In the sequential online stage, we transfer the offline agent safely as the online agent to perform continuous learning and controlling online with significantly improved safety and efficiency. Numerical simulations on IEEE test cases not only demonstrate that the proposed adversarial reinforcement learning algorithm outperforms the state-of-art algorithm, but also show that our proposed two-stage method achieves much better performance than the existing DRL based methods in the online application.Comment: 8 page

Reinforcement Learning with Deep Energy-Based Policies

We propose a method for learning expressive energy-based policies for continuous states and actions, which has been feasible only in tabular domains before. We apply our method to learning maximum entropy policies, resulting into a new algorithm, called soft Q-learning, that expresses the optimal policy via a Boltzmann distribution. We use the recently proposed amortized Stein variational gradient descent to learn a stochastic sampling network that approximates samples from this distribution. The benefits of the proposed algorithm include improved exploration and compositionality that allows transferring skills between tasks, which we confirm in simulated experiments with swimming and walking robots. We also draw a connection to actor-critic methods, which can be viewed performing approximate inference on the corresponding energy-based model

Relative Entropy Regularized Policy Iteration

We present an off-policy actor-critic algorithm for Reinforcement Learning (RL) that combines ideas from gradient-free optimization via stochastic search with learned action-value function. The result is a simple procedure consisting of three steps: i) policy evaluation by estimating a parametric action-value function; ii) policy improvement via the estimation of a local non-parametric policy; and iii) generalization by fitting a parametric policy. Each step can be implemented in different ways, giving rise to several algorithm variants. Our algorithm draws on connections to existing literature on black-box optimization and 'RL as an inference' and it can be seen either as an extension of the Maximum a Posteriori Policy Optimisation algorithm (MPO) [Abdolmaleki et al., 2018a], or as an extension of Trust Region Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) [Abdolmaleki et al., 2017b; Hansen et al., 1997] to a policy iteration scheme. Our comparison on 31 continuous control tasks from parkour suite [Heess et al., 2017], DeepMind control suite [Tassa et al., 2018] and OpenAI Gym [Brockman et al., 2016] with diverse properties, limited amount of compute and a single set of hyperparameters, demonstrate the effectiveness of our method and the state of art results. Videos, summarizing results, can be found at goo.gl/HtvJKR

Merging Deterministic Policy Gradient Estimations with Varied Bias-Variance Tradeoff for Effective Deep Reinforcement Learning

Deep reinforcement learning (DRL) on Markov decision processes (MDPs) with continuous action spaces is often approached by directly training parametric policies along the direction of estimated policy gradients (PGs). Previous research revealed that the performance of these PG algorithms depends heavily on the bias-variance tradeoffs involved in estimating and using PGs. A notable approach towards balancing this tradeoff is to merge both on-policy and off-policy gradient estimations. However existing PG merging methods can be sample inefficient and are not suitable to train deterministic policies directly. To address these issues, this paper introduces elite PGs and strengthens their variance reduction effect by adopting elitism and policy consolidation techniques to regularize policy training based on policy behavioral knowledge extracted from elite trajectories. Meanwhile, we propose a two-step method to merge elite PGs and conventional PGs as a new extension of the conventional interpolation merging method. At both the theoretical and experimental levels, we show that both two-step merging and interpolation merging can induce varied bias-variance tradeoffs during policy training. They enable us to effectively use elite PGs and mitigate their performance impact on trained policies. Our experiments also show that two-step merging can outperform interpolation merging and several state-of-the-art algorithms on six benchmark control tasks

A Convergence Result for Regularized Actor-Critic Methods

In this paper, we present a probability one convergence proof, under suitable conditions, of a certain class of actor-critic algorithms for finding approximate solutions to entropy-regularized MDPs using the machinery of stochastic approximation. To obtain this overall result, we prove the convergence of policy evaluation with general regularizers when using linear approximation architectures and show convergence of entropy-regularized policy improvement