# Bootstrapping Expectiles in Reinforcement Learning

arXiv: https://arxiv.org/abs/2406.04081 · HTML: https://mlsanity.com/paper/2406.04081/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 33 of its 50 references that are in the map.
- First posted on arXiv 6 Jun 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 30 of 33)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Agent57: Outperforming the Atari Human Benchmark](https://mlsanity.com/paper/2003.13350/) (2020)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [Action Robust Reinforcement Learning and Applications in Continuous Control](https://mlsanity.com/paper/1901.09184/) (2019)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [Distributionally Robust Model-Based Offline Reinforcement Learning with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2208.05767/) (2022)
- [Model Selection in Contextual Stochastic Bandit Problems](https://mlsanity.com/paper/2003.01704/) (2020)
- [Statistics and Samples in Distributional Reinforcement Learning](https://mlsanity.com/paper/1902.08102/) (2019)
- [Risk Averse Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1904.00511/) (2019)
- [Tactical Optimism and Pessimism for Deep Reinforcement Learning](https://mlsanity.com/paper/2102.03765/) (2021)
- [Wasserstein Robust Reinforcement Learning](https://mlsanity.com/paper/1907.13196/) (2019)
- [The Curious Price of Distributional Robustness in Reinforcement Learning with a Generative Model](https://mlsanity.com/paper/2305.16589/) (2023)
- [Partial Policy Iteration for L1-Robust Markov Decision Processes](https://mlsanity.com/paper/2006.09484/) (2020)
- [Twice regularized MDPs and the equivalence between robustness and regularization](https://mlsanity.com/paper/2110.06267/) (2021)
- [Efficient Risk-Averse Reinforcement Learning](https://mlsanity.com/paper/2205.05138/) (2022)
- [Towards Safe Reinforcement Learning via Constraining Conditional Value-at-Risk](https://mlsanity.com/paper/2206.04436/) (2022)
- [Distributional Robustness and Regularization in Reinforcement Learning](https://mlsanity.com/paper/2003.02894/) (2020)
- [Regularized Policies are Reward Robust](https://mlsanity.com/paper/2101.07012/) (2021)
- [Mean-Variance Policy Iteration for Risk-Averse Reinforcement Learning](https://mlsanity.com/paper/2004.10888/) (2020)
- [Towards Theoretical Understandings of Robust Markov Decision Processes: Sample Complexity and Asymptotics](https://mlsanity.com/paper/2105.03863/) (2021)
- [Towards Minimax Optimality of Model-based Robust Reinforcement Learning](https://mlsanity.com/paper/2302.05372/) (2023)
- [Your Policy Regularizer is Secretly an Adversary](https://mlsanity.com/paper/2203.12592/) (2022)
- [Efficient Policy Iteration for Robust Markov Decision Processes via Regularization](https://mlsanity.com/paper/2205.14327/) (2022)

## Built on by (most cited first, 1 of 1)

- [Reinforcement learning with an expectile-based objective](https://mlsanity.com/paper/2602.09300/) (2026)

## Abstract (arXiv)

Many classic Reinforcement Learning (RL) algorithms rely on a Bellman operator, which involves an expectation over the next states, leading to the concept of bootstrapping. To introduce a form of pessimism, we propose to replace this expectation with an expectile. In practice, this can be very simply done by replacing the L2 loss with a more general expectile loss for the critic. Introducing pessimism in RL is desirable for various reasons, such as tackling the overestimation problem (for which classic solutions are double Q-learning or the twin-critic approach of TD3) or robust RL (where transitions are adversarial). We study empirically these two cases. For the overestimation problem, we show that the proposed approach, ExpectRL, provides better results than a classic twin-critic. On robust RL benchmarks, involving changes of the environment, we show that our approach is more robust than classic RL algorithms. We also introduce a variation of ExpectRL combined with domain randomization which is competitive with state-of-the-art robust RL agents. Eventually, we also extend ExpectRL with a mechanism for choosing automatically the expectile value, that is the degree of pessimism