# Playing Atari Space Invaders with Sparse Cosine Optimized Policy Evolution

arXiv: https://arxiv.org/abs/2508.08526 · HTML: https://mlsanity.com/paper/2508.08526/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 33 references that are in the map.
- First posted on arXiv 11 Aug 2025.

## Builds on (most cited first, 15 of 15)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (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)
- [Revisiting the Arcade Learning Environment: Evaluation Protocols and Open Problems for General Agents](https://mlsanity.com/paper/1709.06009/) (2017)
- [First return, then explore](https://mlsanity.com/paper/2004.12919/) (2020)
- [Deep Neuroevolution: Genetic Algorithms Are a Competitive Alternative for Training Deep Neural Networks for Reinforcement Learning](https://mlsanity.com/paper/1712.06567/) (2017)
- [Counter-Strike Deathmatch with Large-Scale Behavioural Cloning](https://mlsanity.com/paper/2104.04258/) (2021)
- [Deep Attention Recurrent Q-Network](https://mlsanity.com/paper/1512.01693/) (2015)

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

- [DSLE: A Learning Environment for Dark Souls Boss Encounters](https://mlsanity.com/paper/2608.09902/) (2026)

## Abstract (arXiv)

Evolutionary approaches have previously been shown to be effective learning methods for a diverse set of domains. However, the domain of game-playing poses a particular challenge for evolutionary methods due to the inherently large state space of video games. As the size of the input state expands, the size of the policy must also increase in order to effectively learn the temporal patterns in the game space. Consequently, a larger policy must contain more trainable parameters, exponentially increasing the size of the search space. Any increase in search space is highly problematic for evolutionary methods, as increasing the number of trainable parameters is inversely correlated with convergence speed. To reduce the size of the input space while maintaining a meaningful representation of the original space, we introduce Sparse Cosine Optimized Policy Evolution (SCOPE). SCOPE utilizes the Discrete Cosine Transform (DCT) as a pseudo attention mechanism, transforming an input state into a coefficient matrix. By truncating and applying sparsification to this matrix, we reduce the dimensionality of the input space while retaining the highest energy features of the original input. We demonstrate the effectiveness of SCOPE as the policy for the Atari game Space Invaders. In this task, SCOPE with CMA-ES outperforms evolutionary methods that consider an unmodified input state, such as OpenAI-ES and HyperNEAT. SCOPE also outperforms simple reinforcement learning methods, such as DQN and A3C. SCOPE achieves this result through reducing the input size by 53% from 33,600 to 15,625 then using a bilinear affine mapping of sparse DCT coefficients to policy actions learned by the CMA-ES algorithm.