polarix

Overview

The name polarix draws from the Polaris star system, a guiding star, and ends in 'x' to reflect its ties to the JAX ecosystem.

polarix is an accelerated equilibrium solving and evaluation library for computing interpretable ratings at game-theoretic equilibria.

The game-theoretic approach dynamically adjusts the relevance of each action (e.g. an evaluation task, a candidate model, an agent) based on how they interact with each other. The rating equilibrium that is selected continually adapts to the capability frontiers of each player based on an overarching evaluation objective that you define.

What is polarix for?

• Evaluation: polarix is designed for dynamic evaluation systems where new candidates and tasks are continually introduced and where one may wish to know the value of each candidate and each task.
• Training: polarix can be used to identify frontier candidates and frontier tasks, making training more robust and efficient.
• Research: polarix implements accelerated equilibrium solvers for n-player general-sum games, which can also serve as baselines for game-theory research in equilibrium solving and selection.

Installation

You can install polarix from PyPi:

pip install -U polarix

or from source, with no stability guarantees.

pip install git+git://github.com/google-deepmind/polarix.git

Quick Start

Here's a simple example of how to use polarix to rate agents based on their performance on a set of tasks.

import numpy as np
import polarix as plx

agents = np.array(['skew_a', 'skew_b', 'skew_c', 'weak', 'strong'])
tasks = np.array(['task_a', 'task_b', 'task_c'])
scores = np.asarray([
    [6.0, 4.0, 3.0],  # skew_a
    [3.0, 5.0, 2.0],  # skew_b
    [1.0, 3.0, 7.0],  # skew_c
    [3.0, 4.0, 3.0],  # weak
    [5.0, 4.0, 5.0],  # strong
])
scores_stddev = np.full_like(scores, fill_value=0.1)

# 1. Define the evaluation game from an agent-vs-task score matrix.
# From this agent-vs-task score matrix, we construct a 3-player game between a
#  'task' player and two 'agent' players.
#
# Each agent player chooses an agent and is rewarded for outperforming
#  competition on the task selected by the task player. The task player is
#  rewarded by the agent players' score difference, i.e. separating the agents.
#
# The `plx.agent_vs_task` helper function constructs such a 3-player game from
#  an agent-vs-task score matrix. Instances of `plx.Game` can be constructed
#  directly from payoff tensors as well.
game = plx.agent_vs_task_game(
    agents=agents, tasks=tasks, agent_vs_task=scores, normalizer='winrate'
)

# 2. Solve for the max-entropy correlated equilibrium strategy and ratings.
res = plx.solve(game, plx.ce_maxent)

# 3. Analyze agent ratings in terms of comparative strengths and weaknesses.
chart = plx.plot_rating_contribution(
    game,
    joint=res.joint,
    rating_player=1,
    contrib_player=0,
    use_categorical_contrib=True,
)

Executing chart.display() shows agent ratings, broken down by task.

Each model's total score (red diamond) is the sum of its comparative strengths (positive bars) and weaknesses (negative bars), all measured relative to an equilibrium strategy. By definition of our ratings, the maximum possible rating is zero, achieved by the strong generalist model. The blue dashed line shows the probability that each agent is played at the equilibrium. Note that specialist agents all received significant probability mass at the equilibrium, showing that the top-ranked agent does not dominate competing agents on all tasks.

References

If you find this library useful, please consider citing it:

@inproceedings{
  liu2025reevaluating,
  title={Re-evaluating Open-ended Evaluation of Large Language Models},
  author={Siqi Liu and Ian Gemp and Luke Marris and Georgios Piliouras and Nicolas Heess and Marc Lanctot},
  booktitle={The Thirteenth International Conference on Learning Representations},
  year={2025},
  url={https://openreview.net/forum?id=kbOAIXKWgx}
}

This project also builds on these published works:

• Balduzzi, David, et al. "Re-evaluating evaluation." Advances in Neural Information Processing Systems 31 (2018).
• Gemp, Ian, Luke Marris, and Georgios Piliouras. "Approximating Nash Equilibria in Normal-Form Games via Stochastic Optimization." The Twelfth International Conference on Learning Representations.
• Marris, Luke, et al. "Multi-agent training beyond zero-sum with correlated equilibrium meta-solvers." International Conference on Machine Learning. 2021.
• Gemp, Ian, et al. "Sample-based Approximation of Nash in Large Many-Player Games via Gradient Descent." Proceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems. 2022.

Disclaimer

This is not an officially supported Google product.