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Register a new userOn the Sample Complexity of Batch Reinforcement Learning with Policy-Induced Data
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Chenjun Xiao
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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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.
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We study the optimal sample complexity in large-scale Reinforcement Learning (RL) problems with policy space generalization, i.e. the agent has a prior knowledge that the optimal policy lies in a known policy space. Existing results show that without a generalization model, the sample complexity of an RL algorithm will inevitably depend on the cardinalities of state space and action space, which are intractably large in many practical problems. To avoid such undesirable dependence on the state and action space sizes, this paper proposes a new notion of eluder dimension for the policy space, which characterizes the intrinsic complexity of policy learning in an arbitrary Markov Decision Process (MDP). Using a simulator oracle, we prove a near-optimal sample complexity upper bound that only depends linearly on the eluder dimension. We further prove a similar regret bound in deterministic systems without the simulator.
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.
This paper considers batch Reinforcement Learning (RL) with general value function approximation. Our study investigates the minimal assumptions to reliably estimate/minimize Bellman error, and characterizes the generalization performance by (local) Rademacher complexities of general function classes, which makes initial steps in bridging the gap between statistical learning theory and batch RL. Concretely, we view the Bellman error as a surrogate loss for the optimality gap, and prove the followings: (1) In double sampling regime, the excess risk of Empirical Risk Minimizer (ERM) is bounded by the Rademacher complexity of the function class. (2) In the single sampling regime, sample-efficient risk minimization is not possible without further assumptions, regardless of algorithms. However, with completeness assumptions, the excess risk of FQI and a minimax style algorithm can be again bounded by the Rademacher complexity of the corresponding function classes. (3) Fast statistical rates can be achieved by using tools of local Rademacher complexity. Our analysis covers a wide range of function classes, including finite classes, linear spaces, kernel spaces, sparse linear features, etc.
Most deep reinforcement learning (RL) systems are not able to learn effectively from off-policy data, especially if they cannot explore online in the environment. These are critical shortcomings for applying RL to real-world problems where collecting data is expensive, and models must be tested offline before being deployed to interact with the environment -- e.g. systems that learn from human interaction. Thus, we develop a novel class of off-policy batch RL algorithms, which are able to effectively learn offline, without exploring, from a fixed batch of human interaction data. We leverage models pre-trained on data as a strong prior, and use KL-control to penalize divergence from this prior during RL training. We also use dropout-based uncertainty estimates to lower bound the target Q-values as a more efficient alternative to Double Q-Learning. The algorithms are tested on the problem of open-domain dialog generation -- a challenging reinforcement learning problem with a 20,000-dimensional action space. Using our Way Off-Policy algorithm, we can extract multiple different reward functions post-hoc from collected human interaction data, and learn effectively from all of these. We test the real-world generalization of these systems by deploying them live to converse with humans in an open-domain setting, and demonstrate that our algorithm achieves significant improvements over prior methods in off-policy batch RL.
We tackle the Multi-task Batch Reinforcement Learning problem. Given multiple datasets collected from different tasks, we train a multi-task policy to perform well in unseen tasks sampled from the same distribution. The task identities of the unseen tasks are not provided. To perform well, the policy must infer the task identity from collected transitions by modelling its dependency on states, actions and rewards. Because the different datasets may have state-action distributions with large divergence, the task inference module can learn to ignore the rewards and spuriously correlate $textit{only}$ state-action pairs to the task identity, leading to poor test time performance. To robustify task inference, we propose a novel application of the triplet loss. To mine hard negative examples, we relabel the transitions from the training tasks by approximating their reward functions. When we allow further training on the unseen tasks, using the trained policy as an initialization leads to significantly faster convergence compared to randomly initialized policies (up to $80%$ improvement and across 5 different Mujoco task distributions). We name our method $textbf{MBML}$ ($textbf{M}text{ulti-task}$ $textbf{B}text{atch}$ RL with $textbf{M}text{etric}$ $textbf{L}text{earning}$).
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