[Paper Review] Towards Deployment-Efficient Reinforcement Learning: Lower Bound and Optimality

Jiawei Huang, Jing‐Lin Chen+4 more|arXiv (Cornell University)|Feb 14, 2022

Age of Information Optimization4 citations

TL;DR

This paper formalizes Deployment-Efficient Reinforcement Learning (DE-RL) as an optimization-with-constraints problem, minimizing deployment count $K$ while collecting large batches of trajectories per deployment. It establishes information-theoretic lower bounds of $\Omega(dH)$ and $\widetilde{\Omega}(H)$ for deterministic and general policies, respectively, and proposes algorithms achieving these bounds, demonstrating optimal deployment efficiency in finite-horizon linear MDPs.

ABSTRACT

Deployment efficiency is an important criterion for many real-world applications of reinforcement learning (RL). Despite the community's increasing interest, there lacks a formal theoretical formulation for the problem. In this paper, we propose such a formulation for deployment-efficient RL (DE-RL) from an "optimization with constraints" perspective: we are interested in exploring an MDP and obtaining a near-optimal policy within minimal \emph{deployment complexity}, whereas in each deployment the policy can sample a large batch of data. Using finite-horizon linear MDPs as a concrete structural model, we reveal the fundamental limit in achieving deployment efficiency by establishing information-theoretic lower bounds, and provide algorithms that achieve the optimal deployment efficiency. Moreover, our formulation for DE-RL is flexible and can serve as a building block for other practically relevant settings; we give "Safe DE-RL" and "Sample-Efficient DE-RL" as two examples, which may be worth future investigation.

Motivation & Objective

• To formalize deployment efficiency in RL as a constrained optimization problem minimizing deployments $K$ under large-batch sampling.
• To identify fundamental limits of deployment efficiency via information-theoretic lower bounds in finite-horizon linear MDPs.
• To design algorithms that achieve optimal deployment complexity for both deterministic and general policy deployment settings.
• To extend the DE-RL framework to practical variants like Safe DE-RL and Sample-Efficient DE-RL.

Proposed method

• Formulates DE-RL as minimizing deployment count $K$ under constraints: (a) return an $\varepsilon$-optimal policy after $K$ deployments, and (b) each deployment collects $N$ trajectories with $N$ polynomial in problem parameters.
• Uses finite-horizon linear MDPs as a structural model to derive lower bounds and design algorithms.
• Proposes a deterministic policy algorithm based on Least-Square Value Iteration with reward bonus and layer-by-layer exploration, achieving $O(dH)$ deployments.
• Introduces a novel batched finite-sample version of the Elliptical Potential Lemma as a technical tool for analysis.
• Develops a mixture policy strategy combining pessimistic and optimistic offline algorithms to satisfy monotonic policy improvement constraints.
• Extends results to Safe DE-RL via a policy improvement constraint $J(\pi_{i+1}) \geq J(\pi_i) - \varepsilon$ and to Sample-Efficient DE-RL by bounding $N$.

Experimental results

Research questions

• RQ1 What is the fundamental lower bound on the number of deployments required to achieve $\varepsilon$-optimality in DE-RL?
• RQ2 Can algorithms be designed to achieve the information-theoretic lower bound on deployment complexity?
• RQ3 How does the requirement to deploy only deterministic policies affect the deployment efficiency limit?
• RQ4 What is the trade-off between deployment efficiency and sample efficiency when $N$ is bounded?
• RQ5 How can safety constraints like monotonic policy improvement be integrated into the DE-RL framework?

Key findings

• The paper establishes a tight $\Omega(dH)$ lower bound on deployment complexity for algorithms deploying only deterministic policies in finite-horizon linear MDPs.
• For general policy deployment, the lower bound is $\widetilde{\Omega}(H)$, showing that horizon dependence remains fundamental even with unrestricted policies.
• The proposed algorithm for deterministic policy deployment achieves $O(dH)$ deployments, matching the lower bound and thus proving optimality.
• A novel batched finite-sample version of the Elliptical Potential Lemma is proven as Lemma 4.2, enabling the analysis of the proposed algorithm.
• The mixture policy strategy in Safe DE-RL ensures monotonic policy improvement with high probability by balancing pessimistic and optimistic policies.
• The framework is extensible to Sample-Efficient DE-RL, where $N$ is bounded, and the trade-off between $K$ and $N_0$ remains an open problem.