Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
The impact of uncertainty on regularized learning in games
Authors: Pierre-Louis Cauvin, Davide Legacci, Panayotis Mertikopoulos
ICML 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Our findings reveal that, in a fairly precise sense, uncertainty favors extremes : in any game, regardless of the noise level, every player s trajectory of play reaches an arbitrarily small neighborhood of a pure strategy in finite time (which we estimate). Moreover, even if the player does not ultimately settle at this strategy, they return arbitrarily close to some (possibly different) pure strategy infinitely often. This prompts the question of which sets of pure strategies emerge as robust predictions of learning under uncertainty. We show that (a) the only possible limits of the FTRL dynamics under uncertainty are pure Nash equilibria; and (b) a span of pure strategies is stable and attracting if and only if it is closed under better replies. Finally, we turn to games where the deterministic dynamics are recurrent such as zero-sum games with interior equilibria and show that randomness disrupts this behavior, causing the stochastic dynamics to drift toward the boundary on average. (...) The proof of Proposition 1 is an arduous combination of ItΓ΄ s lemma with elements of convex analysis in the spirit of [13], so we defer it to Appendix C. (...) Our first result for (S-FTRL) indicates a radical departure from the deterministic setting: it shows that, in any game, regardless of initialization, every player reaches an arbitrarily small neighborhood of one of their pure strategies in finite time. Theorem 1. Suppose Assumptions 1 and 2 hold, fix a sufficiently small accuracy threshold Μ > 0, and let (...) The proof of Theorem 1 hinges on crafting a suitable Lyapunov function in the spirit of Imhof [28], and then bounding the action of the infinitesimal generator of the strategy dynamics (14) on said function in order to apply Dynkin s formula on Μi,Μ. These estimates and the resulting calculations are fairly delicate and involved, so we defer all relevant details to Appendix D. |
| Researcher Affiliation | Academia | 1Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, LIG, 38000 Grenoble, France. Correspondence to: Pierre-Louis Cauvin <EMAIL>. |
| Pseudocode | No | The paper describes mathematical dynamics using equations such as (FTRL) and (S-FTRL), and also includes detailed proofs and lemmas in the appendices. However, it does not contain any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing code, nor does it provide any links to code repositories. |
| Open Datasets | No | The paper discusses various game theory concepts such as "zero-sum games," "Matching Pennies," and "Entry Deterrence game" to illustrate theoretical dynamics. It does not refer to any specific empirical datasets or provide access information for any data used in experiments. |
| Dataset Splits | No | The paper focuses on theoretical analysis and does not involve experimental evaluation on datasets, thus no dataset split information is provided. |
| Hardware Specification | No | The paper presents theoretical research and does not describe any experimental hardware used. |
| Software Dependencies | No | The paper focuses on theoretical mathematical analysis and does not mention any specific software or library dependencies with version numbers. |
| Experiment Setup | No | The paper focuses on theoretical analysis of learning dynamics in games and does not describe any empirical experimental setup details such as hyperparameters or training configurations. |