Constraint-based offline reinforcement learning (RL) involves policy constraints or imposing penalties on the value function to mitigate overestimation errors caused by distributional shift. This paper focuses on a limitation in existing offline RL methods with penalized value function, indicating the potential for underestimation bias due to unnecessary bias introduced in the value function. To address this concern, we propose Exclusively Penalized Q-learning (EPQ), which reduces estimation bias in the value function by selectively penalizing states that are prone to inducing estimation errors. Numerical results show that our method significantly reduces underestimation bias and improves performance in various offline control tasks compared to other offline RL methods.

A widely-used actor-critic reinforcement learning algorithm for continuous control, Deep Deterministic Policy Gradients (DDPG), suffers from the overestimation problem, which can negatively affect the performance. Although the state-of-the-art Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm mitigates the overestimation issue, it can lead to a large underestimation bias. In this paper, we propose to use the Boltzmann softmax operator for value function estimation in continuous control. We first theoretically analyze the softmax operator in continuous action space. Then, we uncover an important property of the softmax operator in actor-critic algorithms, i.e., it helps to smooth the optimization landscape, which sheds new light on the benefits of the operator. We also design two new algorithms, Softmax Deep Deterministic Policy Gradients (SD2) and Softmax Deep Double Deterministic Policy Gradients (SD3), by building the softmax operator upon single and double estimators, which can effectively improve the overestimation and underestimation bias. We conduct extensive experiments on challenging continuous control tasks, and results show that SD3 outperforms state-of-the-art methods.

Double Q-learning is a classical method for reducing overestimation bias, which is caused by taking maximum estimated values in the Bellman operation. Its variants in the deep Q-learning paradigm have shown great promise in producing reliable value prediction and improving learning performance. However, as shown by prior work, double Q-learning is not fully unbiased and suffers from underestimation bias. In this paper, we show that such underestimation bias may lead to multiple non-optimal fixed points under an approximate Bellman operator. To address the concerns of converging to non-optimal stationary solutions, we propose a simple but effective approach as a partial fix for the underestimation bias in double Q-learning. This approach leverages an approximate dynamic programming to bound the target value. We extensively evaluate our proposed method in the Atari benchmark tasks and demonstrate its significant improvement over baseline algorithms.

Deterministic policy gradient algorithms for continuous control suffer from value estimation biases that degrade performance. While double critics reduce such biases, the exploration potential of double actors remains underexplored. Building on temporal-difference error-driven regularization (TDDR), a double actor-critic framework, this work introduces enhanced methods to achieve flexible bias control and stronger representation learning. We propose three convex combination strategies, symmetric and asymmetric, that balance pessimistic estimates to mitigate overestimation and optimistic exploration via double actors to alleviate underestimation. A single hyperparameter governs this mechanism, enabling tunable control across the bias spectrum. To further improve performance, we integrate augmented state and action representations into the actor and critic networks. Extensive experiments show that our approach consistently outperforms benchmarks, demonstrating the value of tunable bias and revealing that both overestimation and underestimation can be exploited differently depending on the environment.

It is known that the estimation bias hinges heavily on the ensemble size (i.e.,

We first theoretically analyze the softmax operator in continuous action space.

Constraint-based offline reinforcement learning (RL) involves policy constraints or imposing penalties on the value function to mitigate overestimation errors caused by distributional shift. This paper focuses on a limitation in existing offline RL methods with penalized value function, indicating the potential for underestimation bias due to unnecessary bias introduced in the value function. To address this concern, we propose Exclusively Penalized Q-learning (EPQ), which reduces estimation bias in the value function by selectively penalizing states that are prone to inducing estimation errors. Numerical results show that our method significantly reduces underestimation bias and improves performance in various offline control tasks compared to other offline RL methods.