A Block Coordinate Ascent Algorithm for Mean-Variance Optimization

TL;DR

This paper introduces a model-free block coordinate ascent algorithm for mean-variance optimization, providing finite-sample guarantees and addressing tuning challenges of existing stochastic approximation methods.

Contribution

It develops a novel stochastic block coordinate ascent policy search method with convergence guarantees and finite-sample error bounds for mean-variance optimization.

Findings

Convergence guarantees for the last iteration and randomly selected solutions.

Finite-sample error bounds for local optima.

Validated on several benchmark domains.

Abstract

Risk management in dynamic decision problems is a primary concern in many fields, including financial investment, autonomous driving, and healthcare. The mean-variance function is one of the most widely used objective functions in risk management due to its simplicity and interpretability. Existing algorithms for mean-variance optimization are based on multi-time-scale stochastic approximation, whose learning rate schedules are often hard to tune, and have only asymptotic convergence proof. In this paper, we develop a model-free policy search framework for mean-variance optimization with finite-sample error bound analysis (to local optima). Our starting point is a reformulation of the original mean-variance function with its Fenchel dual, from which we propose a stochastic block coordinate ascent policy search algorithm. Both the asymptotic convergence guarantee of the last iteration's solution and the convergence rate of the randomly picked solution are provided, and their applicability is demonstrated on several benchmark domains.