AlgaeDICE: Policy Gradient from Arbitrary Experience

In many real-world applications of reinforcement learning (RL), interactions with the environment are limited due to cost or feasibility. This presents a challenge to traditional RL algorithms since the max-return objective involves an expectation over on-policy samples. We introduce a new formulation of max-return optimization that allows the problem to be re-expressed by an expectation over an arbitrary behavior-agnostic and off-policy data distribution. We first derive this result by considering a regularized version of the dual max-return objective before extending our findings to unregularized objectives through the use of a Lagrangian formulation of the linear programming characterization of Q-values. We show that, if auxiliary dual variables of the objective are optimized, then the gradient of the off-policy objective is exactly the on-policy policy gradient, without any use of importance weighting. In addition to revealing the appealing theoretical properties of this approach, we also show that it delivers good practical performance.

CAQL: Continuous Action Q-Learning

Value-based reinforcement learning (RL) methods like Q-learning have shown success in a variety of domains. One challenge in applying Q-learning to continuous-action RL problems, however, is the continuous action maximization (max-Q) required for optimal Bellman backup. In this work, we develop CAQL, a (class of) algorithm(s) for continuous-action Q-learning that can use several plug-and-play optimizers for the max-Q problem. Leveraging recent optimization results for deep neural networks, we show that max-Q can be solved optimally using mixed-integer programming (MIP). When the Q-function representation has sufficient power, MIP-based optimization gives rise to better policies and is more robust than approximate methods (e.g., gradient ascent, cross-entropy search). We further develop several techniques to accelerate inference in CAQL, which despite their approximate nature, perform well. We compare CAQL with state-of-the-art RL algorithms on benchmark continuous-control problems that have different degrees of action constraints and show that CAQL outperforms policy-based methods in heavily constrained environments, often dramatically.

Prediction, Consistency, Curvature: Representation Learning for Locally-Linear Control

Many real-world sequential decision-making problems can be formulated as optimal control with high-dimensional observations and unknown dynamics. A promising approach is to embed the high-dimensional observations into a lower-dimensional latent representation space, estimate the latent dynamics model, then utilize this model for control in the latent space. An important open question is how to learn a representation that is amenable to existing control algorithms? In this paper, we focus on learning representations for locally-linear control algorithms, such as iterative LQR (iLQR). By formulating and analyzing the representation learning problem from an optimal control perspective, we establish three underlying principles that the learned representation should comprise: 1) accurate prediction in the observation space, 2) consistency between latent and observation space dynamics, and 3) low curvature in the latent space transitions. These principles naturally correspond to a loss function that consists of three terms: prediction, consistency, and curvature (PCC). Crucially, to make PCC tractable, we derive an amortized variational bound for the PCC loss function. Extensive experiments on benchmark domains demonstrate that the new variational-PCC learning algorithm benefits from significantly more stable and reproducible training, and leads to superior control performance. Further ablation studies give support to the importance of all three PCC components for learning a good latent space for control.

DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections

In many real-world reinforcement learning applications, access to the environment is limited to a fixed dataset, instead of direct (online) interaction with the environment. When using this data for either evaluation or training of a new policy, accurate estimates of discounted stationary distribution ratios -- correction terms which quantify the likelihood that the new policy will experience a certain state-action pair normalized by the probability with which the state-action pair appears in the dataset -- can improve accuracy and performance. In this work, we propose an algorithm, DualDICE, for estimating these quantities. In contrast to previous approaches, our algorithm is agnostic to knowledge of the behavior policy (or policies) used to generate the dataset. Furthermore, it eschews any direct use of importance weights, thus avoiding potential optimization instabilities endemic of previous methods. In addition to providing theoretical guarantees, we present an empirical study of our algorithm applied to off-policy policy evaluation and find that our algorithm significantly improves accuracy compared to existing techniques.

Lyapunov-based Safe Policy Optimization for Continuous Control

We study continuous action reinforcement learning problems in which it is crucial that the agent interacts with the environment only through {\em safe} policies, i.e.,~policies that do not take the agent to undesirable situations. We formulate these problems as {\em constrained} Markov decision processes (CMDPs) and present safe policy optimization algorithms that are based on a {\em Lyapunov} approach to solve them. Our algorithms can use any standard policy gradient (PG) method, such as deep deterministic policy gradient (DDPG) or proximal policy optimization (PPO), to train a neural network policy, while guaranteeing near-constraint satisfaction for every policy update by projecting either the policy parameter or the action onto the set of feasible solutions induced by the state-dependent linearized Lyapunov constraints. Compared to the existing constrained PG algorithms, ours are more data efficient as they are able to utilize both on-policy and off-policy data. Moreover, our action-projection algorithm often leads to less conservative policy updates and allows for natural integration into an end-to-end PG training pipeline. We evaluate our algorithms and compare them with the state-of-the-art baselines on several simulated (MuJoCo) tasks, as well as a real-world indoor robot navigation problem, demonstrating their effectiveness in terms of balancing performance and constraint satisfaction. Videos of the experiments can be found in the following link: https://drive.google.com/file/d/1pzuzFqWIE710bE2U6DmS59AfRzqK2Kek/view?usp=sharing .

A Block Coordinate Ascent Algorithm for Mean-Variance Optimization

Risk management in dynamic decision problems is a primary concern in many fields, including financial investment, autonomous driving, and healthcare. The mean-variance function is one of the most widely used objective functions in risk management due to its simplicity and interpretability. Existing algorithms for mean-variance optimization are based on multi-time-scale stochastic approximation, whose learning rate schedules are often hard to tune, and have only asymptotic convergence proof. In this paper, we develop a model-free policy search framework for mean-variance optimization with finite-sample error bound analysis (to local optima). Our starting point is a reformulation of the original mean-variance function with its Fenchel dual, from which we propose a stochastic block coordinate ascent policy search algorithm. Both the asymptotic convergence guarantee of the last iteration's solution and the convergence rate of the randomly picked solution are provided, and their applicability is demonstrated on several benchmark domains.

Risk-Sensitive Generative Adversarial Imitation Learning

We study risk-sensitive imitation learning where the agent's goal is to perform at least as well as the expert in terms of a risk profile. We first formulate our risk-sensitive imitation learning setting. We consider the generative adversarial approach to imitation learning (GAIL) and derive an optimization problem for our formulation, which we call risk-sensitive GAIL (RS-GAIL). We then derive two different versions of our RS-GAIL optimization problem that aim at matching the risk profiles of the agent and the expert w.r.t. Jensen-Shannon (JS) divergence and Wasserstein distance, and develop risk-sensitive generative adversarial imitation learning algorithms based on these optimization problems. We evaluate the performance of our JS-based algorithm and compare it with GAIL and the risk-averse imitation learning (RAIL) algorithm in two MuJoCo tasks.

More Robust Doubly Robust Off-policy Evaluation

We study the problem of off-policy evaluation (OPE) in reinforcement learning (RL), where the goal is to estimate the performance of a policy from the data generated by another policy(ies). In particular, we focus on the doubly robust (DR) estimators that consist of an importance sampling (IS) component and a performance model, and utilize the low (or zero) bias of IS and low variance of the model at the same time. Although the accuracy of the model has a huge impact on the overall performance of DR, most of the work on using the DR estimators in OPE has been focused on improving the IS part, and not much on how to learn the model. In this paper, we propose alternative DR estimators, called more robust doubly robust (MRDR), that learn the model parameter by minimizing the variance of the DR estimator. We first present a formulation for learning the DR model in RL. We then derive formulas for the variance of the DR estimator in both contextual bandits and RL, such that their gradients w.r.t.~the model parameters can be estimated from the samples, and propose methods to efficiently minimize the variance. We prove that the MRDR estimators are strongly consistent and asymptotically optimal. Finally, we evaluate MRDR in bandits and RL benchmark problems, and compare its performance with the existing methods.

A Lyapunov-based Approach to Safe Reinforcement Learning

In many real-world reinforcement learning (RL) problems, besides optimizing the main objective function, an agent must concurrently avoid violating a number of constraints. In particular, besides optimizing performance it is crucial to guarantee the safety of an agent during training as well as deployment (e.g. a robot should avoid taking actions - exploratory or not - which irrevocably harm its hardware). To incorporate safety in RL, we derive algorithms under the framework of constrained Markov decision problems (CMDPs), an extension of the standard Markov decision problems (MDPs) augmented with constraints on expected cumulative costs. Our approach hinges on a novel \emph{Lyapunov} method. We define and present a method for constructing Lyapunov functions, which provide an effective way to guarantee the global safety of a behavior policy during training via a set of local, linear constraints. Leveraging these theoretical underpinnings, we show how to use the Lyapunov approach to systematically transform dynamic programming (DP) and RL algorithms into their safe counterparts. To illustrate their effectiveness, we evaluate these algorithms in several CMDP planning and decision-making tasks on a safety benchmark domain. Our results show that our proposed method significantly outperforms existing baselines in balancing constraint satisfaction and performance.