Instance-optimality in optimal value estimation: Adaptivity via variance-reduced Q-learning

by   Koulik Khamaru, et al.

Various algorithms in reinforcement learning exhibit dramatic variability in their convergence rates and ultimate accuracy as a function of the problem structure. Such instance-specific behavior is not captured by existing global minimax bounds, which are worst-case in nature. We analyze the problem of estimating optimal Q-value functions for a discounted Markov decision process with discrete states and actions and identify an instance-dependent functional that controls the difficulty of estimation in the ℓ_∞-norm. Using a local minimax framework, we show that this functional arises in lower bounds on the accuracy on any estimation procedure. In the other direction, we establish the sharpness of our lower bounds, up to factors logarithmic in the state and action spaces, by analyzing a variance-reduced version of Q-learning. Our theory provides a precise way of distinguishing "easy" problems from "hard" ones in the context of Q-learning, as illustrated by an ensemble with a continuum of difficulty.



There are no comments yet.


page 1

page 2

page 3

page 4


Variance-reduced Q-learning is minimax optimal

We introduce and analyze a form of variance-reduced Q-learning. For γ-di...

Is Temporal Difference Learning Optimal? An Instance-Dependent Analysis

We address the problem of policy evaluation in discounted Markov decisio...

Optimal functional supervised classification with separation condition

We consider the binary supervised classification problem with the Gaussi...

Accelerated and instance-optimal policy evaluation with linear function approximation

We study the problem of policy evaluation with linear function approxima...

Online Learning with Gaussian Payoffs and Side Observations

We consider a sequential learning problem with Gaussian payoffs and side...

Adapting to Function Difficulty and Growth Conditions in Private Optimization

We develop algorithms for private stochastic convex optimization that ad...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.