Online Regenerative Learning

TL;DR

This paper investigates online linear programming with stochastic inputs, demonstrating that existing algorithms perform well under regenerative inputs and proposing a new trend-adaptive algorithm for non-stationary, trending data.

Contribution

It extends the analysis of online algorithms to regenerative and trending stochastic inputs and introduces a trend-adaptive algorithm for non-stationary environments.

Findings

Regret bounds are similar for regenerative and i.i.d inputs.

Proposed a trend-adaptive algorithm for trending inputs.

Numerical simulations confirm the effectiveness of the algorithms.

Abstract

We study a type of Online Linear Programming (OLP) problem that maximizes the objective function with stochastic inputs. The performance of various algorithms that analyze this type of OLP is well studied when the stochastic inputs follow some i.i.d distribution. The two central questions to ask are: (i) can the algorithms achieve the same efficiency if the stochastic inputs are not i.i.d but still stationary, and (ii) how can we modify our algorithms if we know the stochastic inputs are trendy, hence not stationary. We answer the first question by analyzing a regenerative type of input and show the regrets of two popular algorithms are bounded by the same orders as their i.i.d counterparts. We discuss the second question in the context of linearly growing inputs and propose a trend-adaptive algorithm. We provide numerical simulations to illustrate the performance of our algorithms under both regenerative and trendy inputs.