# Beyond ReLU: Chebyshev-DQN for Enhanced Deep Q-Networks

arXiv: https://arxiv.org/abs/2508.14536 · HTML: https://mlsanity.com/paper/2508.14536/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 4 of its 14 references that are in the map.
- First posted on arXiv 20 Aug 2025.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 4 of 4)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)

## Abstract (arXiv)

The performance of Deep Q-Networks (DQN) is critically dependent on the ability of its underlying neural network to accurately approximate the action-value function. Standard function approximators, such as multi-layer perceptrons, may struggle to efficiently represent the complex value landscapes inherent in many reinforcement learning problems. This paper introduces a novel architecture, the Chebyshev-DQN (Ch-DQN), which integrates a Chebyshev polynomial basis into the DQN framework to create a more effective feature representation. By leveraging the powerful function approximation properties of Chebyshev polynomials, we hypothesize that the Ch-DQN can learn more efficiently and achieve higher performance. We evaluate our proposed model on the CartPole-v1 benchmark and compare it against a standard DQN with a comparable number of parameters. Our results demonstrate that the Ch-DQN with a moderate polynomial degree (N=4) achieves significantly better asymptotic performance, outperforming the baseline by approximately 39%. However, we also find that the choice of polynomial degree is a critical hyperparameter, as a high degree (N=8) can be detrimental to learning. This work validates the potential of using orthogonal polynomial bases in deep reinforcement learning while also highlighting the trade-offs involved in model complexity.