# A Block Coordinate Ascent Algorithm for Mean-Variance Optimization

arXiv: https://arxiv.org/abs/1809.02292 · HTML: https://mlsanity.com/paper/1809.02292/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2018.

## Built on by (most cited first, 11 of 11)

- [Efficient Risk-Averse Reinforcement Learning](https://mlsanity.com/paper/2205.05138/) (2022)
- [Average-Reward Off-Policy Policy Evaluation with Function Approximation](https://mlsanity.com/paper/2101.02808/) (2021)
- [An Alternative to Variance: Gini Deviation for Risk-averse Policy Gradient](https://mlsanity.com/paper/2307.08873/) (2023)
- [Risk-Averse Finetuning of Large Language Models](https://mlsanity.com/paper/2501.06911/) (2025)
- [A unified algorithm framework for mean-variance optimization in discounted Markov decision processes](https://mlsanity.com/paper/2201.05737/) (2022)
- [SAT: Sequential Agent Tuning for Coordinator Free Plug and Play Multi-LLM Training with Monotonic Improvement Guarantees](https://mlsanity.com/paper/2605.05216/) (2026)
- [TDM: Trustworthy Decision-Making via Interpretability Enhancement](https://mlsanity.com/paper/2108.06080/) (2021)
- [Mean-Semivariance Policy Optimization via Risk-Averse Reinforcement Learning](https://mlsanity.com/paper/2206.07376/) (2022)
- [Global Algorithms for Mean-Variance Optimization in Markov Decision Processes](https://mlsanity.com/paper/2302.13710/) (2023)
- [STOPS: Short-Term-based Volatility-controlled Policy Search and its Global Convergence](https://mlsanity.com/paper/2201.09857/) (2022)
- [Measures of Variability for Risk-averse Policy Gradient](https://mlsanity.com/paper/2504.11412/) (2025)

## Abstract (arXiv)

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.