# Competitive Mirror Descent

@article{Schafer2020CompetitiveMD, title={Competitive Mirror Descent}, author={Florian Schafer and Anima Anandkumar and Houman Owhadi}, journal={ArXiv}, year={2020}, volume={abs/2006.10179} }

Constrained competitive optimization involves multiple agents trying to minimize conflicting objectives, subject to constraints. This is a highly expressive modeling language that subsumes most of modern machine learning. In this work we propose competitive mirror descent (CMD): a general method for solving such problems based on first order information that can be obtained by automatic differentiation. First, by adding Lagrange multipliers, we obtain a simplified constraint set with an…

## 7 Citations

### Polymatrix Competitive Gradient Descent

- Computer ScienceArXiv
- 2021

Polymatrix competitive gradient descent is proposed as a method for solving general sum competitive optimization involving arbitrary numbers of agents and it is proved local convergence of PCGD to stable fixed points for n-player general-sum games, and that it does not require adapting the step size to the strength of the player-interactions.

### Robust Reinforcement Learning: A Constrained Game-theoretic Approach

- Computer ScienceL4DC
- 2021

This work proposes a game theoretic framework for robust reinforcement learning that comprises many previous works as special cases and formulate robust RL as a constrained minimax game between the RL agent and an environmental agent which represents uncertainties such as model parameter variations and adversarial disturbances.

### Lifted Primal-Dual Method for Bilinearly Coupled Smooth Minimax Optimization

- Computer ScienceAISTATS
- 2022

The Lifted Primal-Dual (LPD) method is devised, which lifts the objective into an extended form that allows both the smooth terms and the bilinear term to be handled optimally and seamlessly with the same primal-dual framework.

### Lyapunov Exponents for Diversity in Differentiable Games

- Computer ScienceAAMAS
- 2022

Theoretical motivation for the method is given by leveraging machinery from the field of dynamical systems, and it is empirically evaluated by finding diverse solutions in the iterated prisoners’ dilemma and relevant machine learning problems including generative adversarial networks.

### Complex Momentum for Optimization in Games

- Computer ScienceAISTATS
- 2022

It is empirically demon-strate that complex-valued momentum can improve convergence in realistic adversarial games—like generative adversarial networks— by showing better solutions with an almost identical computational cost.

### Complex Momentum for Learning in Games

- Computer ScienceArXiv
- 2021

It is empirically demonstrate that complex-valued momentum can improve convergence in adversarial games—like generative adversarial networks—by showing it can find better solutions with an almost identical computational cost.

### COLA: Consistent Learning with Opponent-Learning Awareness

- EconomicsICML
- 2022

Learning in general-sum games is unstable and frequently leads to socially undesirable (Pareto-dominated) outcomes. To mitigate this, Learning with Opponent-Learning Awareness (LOLA) introduced…

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