Competing with stationary prediction strategies

TL;DR

This paper introduces stationary prediction strategies and develops an algorithm that asymptotically matches the performance of the best such strategy without assuming environment stationarity.

Contribution

It constructs a prediction algorithm that competes with the best continuous stationary strategies in non-stationary environments under mild assumptions.

Findings

Algorithm asymptotically matches the best stationary strategy

No stochastic assumptions about the environment are required

Stationarity of strategies does not depend on environment stationarity

Abstract

In this paper we introduce the class of stationary prediction strategies and construct a prediction algorithm that asymptotically performs as well as the best continuous stationary strategy. We make mild compactness assumptions but no stochastic assumptions about the environment. In particular, no assumption of stationarity is made about the environment, and the stationarity of the considered strategies only means that they do not depend explicitly on time; we argue that it is natural to consider only stationary strategies even for highly non-stationary environments.