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Register a new userOn the Sample Complexity of Reinforcement Learning with Policy Space Generalization
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Wenlong Mou
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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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.
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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.
Standard deep reinforcement learning algorithms use a shared representation for the policy and value function, especially when training directly from images. However, we argue that more information is needed to accurately estimate the value function than to learn the optimal policy. Consequently, the use of a shared representation for the policy and value function can lead to overfitting. To alleviate this problem, we propose two approaches which are combined to create IDAAC: Invariant Decoupled Advantage Actor-Critic. First, IDAAC decouples the optimization of the policy and value function, using separate networks to model them. Second, it introduces an auxiliary loss which encourages the representation to be invariant to task-irrelevant properties of the environment. IDAAC shows good generalization to unseen environments, achieving a new state-of-the-art on the Procgen benchmark and outperforming popular methods on DeepMind Control tasks with distractors. Our implementation is available at https://github.com/rraileanu/idaac.
While recent progress has spawned very powerful machine learning systems, those agents remain extremely specialized and fail to transfer the knowledge they gain to similar yet unseen tasks. In this paper, we study a simple reinforcement learning problem and focus on learning policies that encode the proper invariances for generalization to different settings. We evaluate three potential methods for policy generalization: data augmentation, meta-learning and adversarial training. We find our data augmentation method to be effective, and study the potential of meta-learning and adversarial learning as alternative task-agnostic approaches.
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.
Progress in deep reinforcement learning (RL) research is largely enabled by benchmark task environments. However, analyzing the nature of those environments is often overlooked. In particular, we still do not have agreeable ways to measure the difficulty or solvability of a task, given that each has fundamentally different actions, observations, dynamics, rewards, and can be tackled with diverse RL algorithms. In this work, we propose policy information capacity (PIC) -- the mutual information between policy parameters and episodic return -- and policy-optimal information capacity (POIC) -- between policy parameters and episodic optimality -- as two environment-agnostic, algorithm-agnostic quantitative metrics for task difficulty. Evaluating our metrics across toy environments as well as continuous control benchmark tasks from OpenAI Gym and DeepMind Control Suite, we empirically demonstrate that these information-theoretic metrics have higher correlations with normalized task solvability scores than a variety of alternatives. Lastly, we show that these metrics can also be used for fast and compute-efficient optimizations of key design parameters such as reward shaping, policy architectures, and MDP properties for better solvability by RL algorithms without ever running full RL experiments.
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