Minimax Learning for Remote Prediction

TL;DR

This paper introduces a minimax approach to remote supervised learning with rate constraints, establishing bounds and methods for near-optimal prediction under communication limitations.

Contribution

It formulates remote prediction as a minimax noisy source coding problem and develops a near-optimal design framework for rate-constrained learning.

Findings

Establishes information-theoretic bounds on risk-rate trade-offs.

Proposes a method for designing near-optimal descriptor-estimator pairs.

Shows naive compression schemes are generally suboptimal.

Abstract

The classical problem of supervised learning is to infer an accurate predictor of a target variable $Y$ from a measured variable $X$ by using a finite number of labeled training samples. Motivated by the increasingly distributed nature of data and decision making, in this paper we consider a variation of this classical problem in which the prediction is performed remotely based on a rate-constrained description $M$ of $X$. Upon receiving $M$, the remote node computes an estimate $\hat Y$ of $Y$. We follow the recent minimax approach to study this learning problem and show that it corresponds to a one-shot minimax noisy source coding problem. We then establish information theoretic bounds on the risk-rate Lagrangian cost and a general method to design a near-optimal descriptor-estimator pair, which can be viewed as a rate-constrained analog to the maximum conditional entropy principle used in the classical minimax learning problem. Our results show that a naive estimate-compress scheme for rate-constrained prediction is not in general optimal.