A Few Expert Queries Suffices for Sample-Efficient RL with Resets and Linear Value Approximation

• URL: http://arxiv.org/abs/2207.08342v1
• Date: Mon, 18 Jul 2022 01:39:13 GMT
• Title: A Few Expert Queries Suffices for Sample-Efficient RL with Resets and Linear Value Approximation
• Authors: Philip Amortila, Nan Jiang, Dhruv Madeka, Dean P. Foster
• Abstract summary: We study sample-efficient Reinforcement Learning (RL) in settings where only the optimal value function is assumed to be linearlyrealizable. We present a statistically and computationally efficient algorithm (Delphi) for blending exploration with expert queries. Delphi requires $tildemathcalO(d)$ expert queries and a $textttpoly(d,|mathcalA|,1/varepsilon)$ amount of exploratory samples to provably recover an $varepsilon$suboptimal policy.
• Score: 16.29514743112387
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The current paper studies sample-efficient Reinforcement Learning (RL) in settings where only the optimal value function is assumed to be linearly-realizable. It has recently been understood that, even under this seemingly strong assumption and access to a generative model, worst-case sample complexities can be prohibitively (i.e., exponentially) large. We investigate the setting where the learner additionally has access to interactive demonstrations from an expert policy, and we present a statistically and computationally efficient algorithm (Delphi) for blending exploration with expert queries. In particular, Delphi requires $\tilde{\mathcal{O}}(d)$ expert queries and a $\texttt{poly}(d,H,|\mathcal{A}|,1/\varepsilon)$ amount of exploratory samples to provably recover an $\varepsilon$-suboptimal policy. Compared to pure RL approaches, this corresponds to an exponential improvement in sample complexity with surprisingly-little expert input. Compared to prior imitation learning (IL) approaches, our required number of expert demonstrations is independent of $H$ and logarithmic in $1/\varepsilon$, whereas all prior work required at least linear factors of both in addition to the same dependence on $d$. Towards establishing the minimal amount of expert queries needed, we show that, in the same setting, any learner whose exploration budget is polynomially-bounded (in terms of $d,H,$ and $|\mathcal{A}|$) will require at least $\tilde\Omega(\sqrt{d})$ oracle calls to recover a policy competing with the expert's value function. Under the weaker assumption that the expert's policy is linear, we show that the lower bound increases to $\tilde\Omega(d)$.

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