Saved in:
Bibliographic Details
Main Authors: Xu, R., Yachbes, E., Zhang, J.
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2604.25045
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908997064327168
author Xu, R.
Yachbes, E.
Zhang, J.
author_facet Xu, R.
Yachbes, E.
Zhang, J.
contents Our paper studies the setting of players using no-regret algorithms in various two-player games. We address whether having stronger regret guarantees or playing against an opponent with weaker regret guarantees yields higher utilities for the player in question. We consider a hierarchy of algorithms from weakest to strongest: uniform random play, no-regret, and no-swap-regret. We find, counterintuitively, that in many games, no-swap-regret is a worse choice for players (and gives better utility for their opponents). We find the root cause of this phenomenon to be a difference in effective learning rate between the two algorithms, where the no-swap-regret algorithms learn $N$ times slower than no-regret algorithms. To address this, we attempt to equalize learning rates, leading to closer utility between no-regret and no-swap-regret players. Finally, we show that for certain random games with $7$ actions per player, no-swap-regret algorithms can perform noticeably better than no-regret algorithms in a manner that cannot be explained away by unfairly adjusted learning rates.
format Preprint
id arxiv_https___arxiv_org_abs_2604_25045
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Hierarchies of No-regret Algorithms
Xu, R.
Yachbes, E.
Zhang, J.
Computer Science and Game Theory
Our paper studies the setting of players using no-regret algorithms in various two-player games. We address whether having stronger regret guarantees or playing against an opponent with weaker regret guarantees yields higher utilities for the player in question. We consider a hierarchy of algorithms from weakest to strongest: uniform random play, no-regret, and no-swap-regret. We find, counterintuitively, that in many games, no-swap-regret is a worse choice for players (and gives better utility for their opponents). We find the root cause of this phenomenon to be a difference in effective learning rate between the two algorithms, where the no-swap-regret algorithms learn $N$ times slower than no-regret algorithms. To address this, we attempt to equalize learning rates, leading to closer utility between no-regret and no-swap-regret players. Finally, we show that for certain random games with $7$ actions per player, no-swap-regret algorithms can perform noticeably better than no-regret algorithms in a manner that cannot be explained away by unfairly adjusted learning rates.
title Hierarchies of No-regret Algorithms
topic Computer Science and Game Theory
url https://arxiv.org/abs/2604.25045