Asymptotic Instance-Optimal Algorithms for Interactive Decision Making

06/06/2022
by   Kefan Dong, et al.
0

Past research on interactive decision making problems (bandits, reinforcement learning, etc.) mostly focuses on the minimax regret that measures the algorithm's performance on the hardest instance. However, an ideal algorithm should adapt to the complexity of a particular problem instance and incur smaller regrets on easy instances than worst-case instances. In this paper, we design the first asymptotic instance-optimal algorithm for general interactive decision making problems with finite number of decisions under mild conditions. On every instance f, our algorithm outperforms all consistent algorithms (those achieving non-trivial regrets on all instances), and has asymptotic regret 𝒞(f) ln n, where 𝒞(f) is an exact characterization of the complexity of f. The key step of the algorithm involves hypothesis testing with active data collection. It computes the most economical decisions with which the algorithm collects observations to test whether an estimated instance is indeed correct; thus, the complexity 𝒞(f) is the minimum cost to test the instance f against other instances. Our results, instantiated on concrete problems, recover the classical gap-dependent bounds for multi-armed bandits [Lai and Robbins, 1985] and prior works on linear bandits [Lattimore and Szepesvari, 2017], and improve upon the previous best instance-dependent upper bound [Xu et al., 2021] for reinforcement learning.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/24/2023

Instance-Optimality in Interactive Decision Making: Toward a Non-Asymptotic Theory

We consider the development of adaptive, instance-dependent algorithms f...
research
10/07/2020

Instance-Dependent Complexity of Contextual Bandits and Reinforcement Learning: A Disagreement-Based Perspective

In the classical multi-armed bandit problem, instance-dependent algorith...
research
03/18/2022

The price of unfairness in linear bandits with biased feedback

Artificial intelligence is increasingly used in a wide range of decision...
research
10/14/2016

The End of Optimism? An Asymptotic Analysis of Finite-Armed Linear Bandits

Stochastic linear bandits are a natural and simple generalisation of fin...
research
03/12/2022

Instance-Dependent Regret Analysis of Kernelized Bandits

We study the kernelized bandit problem, that involves designing an adapt...
research
10/23/2020

Instance-Wise Minimax-Optimal Algorithms for Logistic Bandits

Logistic Bandits have recently attracted substantial attention, by provi...
research
12/28/2021

Learning Across Bandits in High Dimension via Robust Statistics

Decision-makers often face the "many bandits" problem, where one must si...

Please sign up or login with your details

Forgot password? Click here to reset