# Learning the Expected Core of Strictly Convex Stochastic Cooperative Games

arXiv: https://arxiv.org/abs/2402.07067 · HTML: https://mlsanity.com/paper/2402.07067/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 10 Feb 2024.

## Builds on (most cited first, 14 of 14)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Counterfactual Multi-Agent Policy Gradients](https://mlsanity.com/paper/1705.08926/) (2017)
- [Value-Decomposition Networks For Cooperative Multi-Agent Learning](https://mlsanity.com/paper/1706.05296/) (2017)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Bandits and Experts in Metric Spaces](https://mlsanity.com/paper/1312.1277/) (2013)
- [Bounding the Estimation Error of Sampling-based Shapley Value Approximation](https://mlsanity.com/paper/1306.4265/) (2013)
- [Approximating the Shapley Value without Marginal Contributions](https://mlsanity.com/paper/2302.00736/) (2023)
- [SHAQ: Incorporating Shapley Value Theory into Multi-Agent Q-Learning](https://mlsanity.com/paper/2105.15013/) (2021)
- [Approximating the Core via Iterative Coalition Sampling](https://mlsanity.com/paper/2402.03928/) (2024)
- [Payoff distribution in robust coalitional games on time-varying networks](https://mlsanity.com/paper/2009.03783/) (2020)
- [Robust Newsvendor Games with Ambiguity in Demand Distributions](https://mlsanity.com/paper/1403.5906/) (2014)
- [Probabilistically robust stabilizing allocations in uncertain coalitional games](https://mlsanity.com/paper/2203.11322/) (2022)
- [Distributionally robust stability of payoff allocations in stochastic coalitional games](https://mlsanity.com/paper/2304.01786/) (2023)

## Abstract (arXiv)

Reward allocation, also known as the credit assignment problem, has been an important topic in economics, engineering, and machine learning. An important concept in reward allocation is the core, which is the set of stable allocations where no agent has the motivation to deviate from the grand coalition. In previous works, computing the core requires either knowledge of the reward function in deterministic games or the reward distribution in stochastic games. However, this is unrealistic, as the reward function or distribution is often only partially known and may be subject to uncertainty. In this paper, we consider the core learning problem in stochastic cooperative games, where the reward distribution is unknown. Our goal is to learn the expected core, that is, the set of allocations that are stable in expectation, given an oracle that returns a stochastic reward for an enquired coalition each round. Within the class of strictly convex games, we present an algorithm named textttCommon-Points-Picking that returns a point in the expected core given a polynomial number of samples, with high probability. To analyse the algorithm, we develop a new extension of the separation hyperplane theorem for multiple convex sets.