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Register a new userOn the Optimality of Batch Policy Optimization Algorithms
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Chenjun Xiao
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Batch policy optimization considers leveraging existing data for policy construction before interacting with an environment. Although interest in this problem has grown significantly in recent years, its theoretical foundations remain under-developed. To advance the understanding of this problem, we provide three results that characterize the limits and possibilities of batch policy optimization in the finite-armed stochastic bandit setting. First, we introduce a class of confidence-adjusted index algorithms that unifies optimistic and pessimistic principles in a common framework, which enables a general analysis. For this family, we show that any confidence-adjusted index algorithm is minimax optimal, whether it be optimistic, pessimistic or neutral. Our analysis reveals that instance-dependent optimality, commonly used to establish optimality of on-line stochastic bandit algorithms, cannot be achieved by any algorithm in the batch setting. In particular, for any algorithm that performs optimally in some environment, there exists another environment where the same algorithm suffers arbitrarily larger regret. Therefore, to establish a framework for distinguishing algorithms, we introduce a new weighted-minimax criterion that considers the inherent difficulty of optimal value prediction. We demonstrate how this criterion can be used to justify commonly used pessimistic principles for batch policy optimization.
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In batch reinforcement learning (RL), one often constrains a learned policy to be close to the behavior (data-generating) policy, e.g., by constraining the learned action distribution to differ from the behavior policy by some maximum degree that is the same at each state. This can cause batch RL to be overly conservative, unable to exploit large policy changes at frequently-visited, high-confidence states without risking poor performance at sparsely-visited states. To remedy this, we propose residual policies, where the allowable deviation of the learned policy is state-action-dependent. We derive a new for RL method, BRPO, which learns both the policy and allowable deviation that jointly maximize a lower bound on policy performance. We show that BRPO achieves the state-of-the-art performance in a number of tasks.
We present two algorithms for Bayesian optimization in the batch feedback setting, based on Gaussian process upper confidence bound and Thompson sampling approaches, along with frequentist regret guarantees and numerical results.
We study the fundamental question of the sample complexity of learning a good policy in finite Markov decision processes (MDPs) when the data available for learning is obtained by following a logging policy that must be chosen without knowledge of the underlying MDP. Our main results show that the sample complexity, the minimum number of transitions necessary and sufficient to obtain a good policy, is an exponential function of the relevant quantities when the planning horizon $H$ is finite. In particular, we prove that the sample complexity of obtaining $epsilon$-optimal policies is at least $Omega(mathrm{A}^{min(mathrm{S}-1, H+1)})$ for $gamma$-discounted problems, where $mathrm{S}$ is the number of states, $mathrm{A}$ is the number of actions, and $H$ is the effective horizon defined as $H=lfloor tfrac{ln(1/epsilon)}{ln(1/gamma)} rfloor$; and it is at least $Omega(mathrm{A}^{min(mathrm{S}-1, H)}/varepsilon^2)$ for finite horizon problems, where $H$ is the planning horizon of the problem. This lower bound is essentially matched by an upper bound. For the average-reward setting we show that there is no algorithm finding $epsilon$-optimal policies with a finite amount of data.
Off-policy Reinforcement Learning (RL) holds the promise of better data efficiency as it allows sample reuse and potentially enables safe interaction with the environment. Current off-policy policy gradient methods either suffer from high bias or high variance, delivering often unreliable estimates. The price of inefficiency becomes evident in real-world scenarios such as interaction-driven robot learning, where the success of RL has been rather limited, and a very high sample cost hinders straightforward application. In this paper, we propose a nonparametric Bellman equation, which can be solved in closed form. The solution is differentiable w.r.t the policy parameters and gives access to an estimation of the policy gradient. In this way, we avoid the high variance of importance sampling approaches, and the high bias of semi-gradient methods. We empirically analyze the quality of our gradient estimate against state-of-the-art methods, and show that it outperforms the baselines in terms of sample efficiency on classical control tasks.
Recent years have witnessed a tremendous improvement of deep reinforcement learning. However, a challenging problem is that an agent may suffer from inefficient exploration, particularly for on-policy methods. Previous exploration methods either rely on complex structure to estimate the novelty of states, or incur sensitive hyper-parameters causing instability. We propose an efficient exploration method, Multi-Path Policy Optimization (MPPO), which does not incur high computation cost and ensures stability. MPPO maintains an efficient mechanism that effectively utilizes a population of diverse policies to enable better exploration, especially in sparse environments. We also give a theoretical guarantee of the stable performance. We build our scheme upon two widely-adopted on-policy methods, the Trust-Region Policy Optimization algorithm and Proximal Policy Optimization algorithm. We conduct extensive experiments on several MuJoCo tasks and their sparsified variants to fairly evaluate the proposed method. Results show that MPPO significantly outperforms state-of-the-art exploration methods in terms of both sample efficiency and final performance.
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