# Variance Penalized On-Policy and Off-Policy Actor-Critic

arXiv: https://arxiv.org/abs/2102.01985 · HTML: https://mlsanity.com/paper/2102.01985/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 47 references that are in the map.
- First posted on arXiv 3 Feb 2021.

## Builds on (most cited first, 14 of 14)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [Safe and Efficient Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1606.02647/) (2016)
- [Risk-sensitive Reinforcement Learning](https://mlsanity.com/paper/1311.2097/) (2013)
- [Optimizing the CVaR via Sampling](https://mlsanity.com/paper/1404.3862/) (2014)
- [Algorithms for CVaR Optimization in MDPs](https://mlsanity.com/paper/1406.3339/) (2014)
- [Risk-Averse Trust Region Optimization for Reward-Volatility Reduction](https://mlsanity.com/paper/1912.03193/) (2019)
- [Variance-Constrained Actor-Critic Algorithms for Discounted and Average Reward MDPs](https://mlsanity.com/paper/1403.6530/) (2014)
- [A Greedy Approach to Adapting the Trace Parameter for Temporal Difference Learning](https://mlsanity.com/paper/1607.00446/) (2016)
- [Entropic Risk Measure in Policy Search](https://mlsanity.com/paper/1906.09090/) (2019)
- [Variance Adjusted Actor Critic Algorithms](https://mlsanity.com/paper/1310.3697/) (2013)

## Built on by (most cited first, 10 of 10)

- [Risk-Aware Transfer in Reinforcement Learning using Successor Features](https://mlsanity.com/paper/2105.14127/) (2021)
- [Robust Reinforcement Learning with Distributional Risk-averse formulation](https://mlsanity.com/paper/2206.06841/) (2022)
- [Absolute Policy Optimization](https://mlsanity.com/paper/2310.13230/) (2023)
- [Adaptive Exploration for Data-Efficient General Value Function Evaluations](https://mlsanity.com/paper/2405.07838/) (2024)
- [A Unified Off-Policy Evaluation Approach for General Value Function](https://mlsanity.com/paper/2107.02711/) (2021)
- [TRAM: Test-Time Risk Adaptation with Mixture of Agents](https://mlsanity.com/paper/2408.08812/) (2024)
- [Learning Individual Policies in Large Multi-agent Systems through Local Variance Minimization](https://mlsanity.com/paper/2212.13379/) (2022)
- [Taylor TD-learning](https://mlsanity.com/paper/2302.14182/) (2023)
- [Nonparametric Variance-Penalized Actor-Critic: Statistical Inference for Risk-Sensitive Reinforcement Learning](https://mlsanity.com/paper/2609.14327/) (2026)
- [When Does Action Credit Need Updating?](https://mlsanity.com/paper/2609.29007/) (2026)

## Abstract (arXiv)

Reinforcement learning algorithms are typically geared towards optimizing the expected return of an agent. However, in many practical applications, low variance in the return is desired to ensure the reliability of an algorithm. In this paper, we propose on-policy and off-policy actor-critic algorithms that optimize a performance criterion involving both mean and variance in the return. Previous work uses the second moment of return to estimate the variance indirectly. Instead, we use a much simpler recently proposed direct variance estimator which updates the estimates incrementally using temporal difference methods. Using the variance-penalized criterion, we guarantee the convergence of our algorithm to locally optimal policies for finite state action Markov decision processes. We demonstrate the utility of our algorithm in tabular and continuous MuJoCo domains. Our approach not only performs on par with actor-critic and prior variance-penalization baselines in terms of expected return, but also generates trajectories which have lower variance in the return.