# Consensus Multiplicative Weights Update: Learning to Learn using Projector-based Game Signatures

arXiv: https://arxiv.org/abs/2106.02615 · HTML: https://mlsanity.com/paper/2106.02615/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 39 references that are in the map.
- First posted on arXiv 4 Jun 2021.

## Builds on (most cited first, 19 of 19)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [A Unified Game-Theoretic Approach to Multiagent Reinforcement Learning](https://mlsanity.com/paper/1711.00832/) (2017)
- [Training GANs with Optimism](https://mlsanity.com/paper/1711.00141/) (2017)
- [Learning to Optimize](https://mlsanity.com/paper/1606.01885/) (2016)
- [Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile](https://mlsanity.com/paper/1807.02629/) (2018)
- [Cycles in adversarial regularized learning](https://mlsanity.com/paper/1709.02738/) (2017)
- [The Mechanics of n-Player Differentiable Games](https://mlsanity.com/paper/1802.05642/) (2018)
- [The Numerics of GANs](https://mlsanity.com/paper/1705.10461/) (2017)
- [Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max Optimization](https://mlsanity.com/paper/1807.04252/) (2018)
- [Open-ended Learning in Symmetric Zero-sum Games](https://mlsanity.com/paper/1901.08106/) (2019)
- [On the convergence of single-call stochastic extra-gradient methods](https://mlsanity.com/paper/1908.08465/) (2019)
- [Negative Momentum for Improved Game Dynamics](https://mlsanity.com/paper/1807.04740/) (2018)
- [Differentiable Game Mechanics](https://mlsanity.com/paper/1905.04926/) (2019)
- [Training Stronger Baselines for Learning to Optimize](https://mlsanity.com/paper/2010.09089/) (2020)
- [Last iterate convergence in no-regret learning: constrained min-max optimization for convex-concave landscapes](https://mlsanity.com/paper/2002.06768/) (2020)
- [Chaos, Extremism and Optimism: Volume Analysis of Learning in Games](https://mlsanity.com/paper/2005.13996/) (2020)
- [Strategic Decompositions of Normal Form Games: Zero-sum Games and Potential Games](https://mlsanity.com/paper/1602.06648/) (2016)

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

- [Multi-agent Performative Prediction: From Global Stability and Optimality to Chaos](https://mlsanity.com/paper/2201.10483/) (2022)

## Abstract (arXiv)

Cheung and Piliouras (2020) recently showed that two variants of the Multiplicative Weights Update method - OMWU and MWU - display opposite convergence properties depending on whether the game is zero-sum or cooperative. Inspired by this work and the recent literature on learning to optimize for single functions, we introduce a new framework for learning last-iterate convergence to Nash Equilibria in games, where the update rule's coefficients (learning rates) along a trajectory are learnt by a reinforcement learning policy that is conditioned on the nature of the game: textitthe game signature. We construct the latter using a new decomposition of two-player games into eight components corresponding to commutative projection operators, generalizing and unifying recent game concepts studied in the literature. We compare the performance of various update rules when their coefficients are learnt, and show that the RL policy is able to exploit the game signature across a wide range of game types. In doing so, we introduce CMWU, a new algorithm that extends consensus optimization to the constrained case, has local convergence guarantees for zero-sum bimatrix games, and show that it enjoys competitive performance on both zero-sum games with constant coefficients and across a spectrum of games when its coefficients are learnt.