In this work, we study algorithms for learning in infinite-horizon undiscounted Markov decision processes (MDPs) with function approximation. We first show that the regret analysis of the Politex algorithm (a version of regularized policy iteration)
can be sharpened from $O(T^{3/4})$ to $O(sqrt{T})$ under nearly identical assumptions, and instantiate the bound with linear function approximation. Our result provides the first high-probability $O(sqrt{T})$ regret bound for a computationally efficient algorithm in this setting. The exact implementation of Politex with neural network function approximation is inefficient in terms of memory and computation. Since our analysis suggests that we need to approximate the average of the action-value functions of past policies well, we propose a simple efficient implementation where we train a single Q-function on a replay buffer with past data. We show that this often leads to superior performance over other implementation choices, especially in terms of wall-clock time. Our work also provides a novel theoretical justification for using experience replay within policy iteration algorithms.
Many reinforcement learning algorithms can be seen
This work focuses on off-policy evaluation (OPE) with function approximation in infinite-horizon undiscounted Markov decision processes (MDPs). For MDPs that are ergodic and linear (i.e. where rewards and dynamics are linear in some known features),
we provide the first finite-sample OPE error bound, extending existing results beyond the episodic and discounted cases. In a more general setting, when the feature dynamics are approximately linear and for arbitrary rewards, we propose a new approach for estimating stationary distributions with function approximation. We formulate this problem as finding the maximum-entropy distribution subject to matching feature expectations under empirical dynamics. We show that this results in an exponential-family distribution whose sufficient statistics are the features, paralleling maximum-entropy approaches in supervised learning. We demonstrate the effectiveness of the proposed OPE approaches in multiple environments.
Model-free reinforcement learning algorithms combined with value function approximation have recently achieved impressive performance in a variety of application domains. However, the theoretical understanding of such algorithms is limited, and exist
ing results are largely focused on episodic or discounted Markov decision processes (MDPs). In this work, we present adaptive approximate policy iteration (AAPI), a learning scheme which enjoys a $tilde{O}(T^{2/3})$ regret bound for undiscounted, continuing learning in uniformly ergodic MDPs. This is an improvement over the best existing bound of $tilde{O}(T^{3/4})$ for the average-reward case with function approximation. Our algorithm and analysis rely on online learning techniques, where value functions are treated as losses. The main technical novelty is the use of a data-dependent adaptive learning rate coupled with a so-called optimistic prediction of upcoming losses. In addition to theoretical guarantees, we demonstrate the advantages of our approach empirically on several environments.
We study algorithms for average-cost reinforcement learning problems with value function approximation. Our starting point is the recently proposed POLITEX algorithm, a version of policy iteration where the policy produced in each iteration is near-o
ptimal in hindsight for the sum of all past value function estimates. POLITEX has sublinear regret guarantees in uniformly-mixing MDPs when the value estimation error can be controlled, which can be satisfied if all policies sufficiently explore the environment. Unfortunately, this assumption is often unrealistic. Motivated by the rapid growth of interest in developing policies that learn to explore their environment in the lack of rewards (also known as no-reward learning), we replace the previous assumption that all policies explore the environment with that a single, sufficiently exploring policy is available beforehand. The main contribution of the paper is the modification of POLITEX to incorporate such an exploration policy in a way that allows us to obtain a regret guarantee similar to the previous one but without requiring that all policies explore environment. In addition to the novel theoretical guarantees, we demonstrate the benefits of our scheme on environments which are difficult to explore using simple schemes like dithering. While the solution we obtain may not achieve the best possible regret, it is the first result that shows how to control the regret in the presence of function approximation errors on problems where exploration is nontrivial. Our approach can also be seen as a way of reducing the problem of minimizing the regret to learning a good exploration policy. We believe that modular approaches like ours can be highly beneficial in tackling harder control problems.
Training robots with physical bodies requires developing new methods and action representations that allow the learning agents to explore the space of policies efficiently. This work studies sample-efficient learning of complex policies in the contex
t of robot table tennis. It incorporates learning into a hierarchical control framework using a model-free strategy layer (which requires complex reasoning about opponents that is difficult to do in a model-based way), model-based prediction of external objects (which are difficult to control directly with analytic control methods, but governed by learnable and relatively simple laws of physics), and analytic controllers for the robot itself. Human demonstrations are used to train dynamics models, which together with the analytic controller allow any robot that is physically capable to play table tennis without training episodes. Using only about 7,000 demonstrated trajectories, a striking policy can hit ball targets with about 20 cm error. Self-play is used to train cooperative and adversarial strategies on top of model-based striking skills trained from human demonstrations. After only about 24,000 strikes in self-play the agent learns to best exploit the human dynamics models for longer cooperative games. Further experiments demonstrate that more flexible variants of the policy can discover new strikes not demonstrated by humans and achieve higher performance at the expense of lower sample-efficiency. Experiments are carried out in a virtual reality environment using sensory observations that are obtainable in the real world. The high sample-efficiency demonstrated in the evaluations show that the proposed method is suitable for learning directly on physical robots without transfer of models or policies from simulation. Supplementary material available at https://sites.google.com/view/robottabletennis
