2026-09-19T22:36:19Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1502272023-04-01T03:38:16Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Daskalakis, Constantinos
Fishelson, Maxwell K.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2023-03-31T14:41:01Z
2023-03-31T14:41:01Z
2023-02
2023-02-28T14:36:07.020Z
https://hdl.handle.net/1721.1/150227
This thesis investigates the regret performance of no-regret learning algorithms in the competitive, though not fully-adversarial, environment of games. We establish exponential improvements on previously best-known external and internal regret bounds for these settings.
We show that Optimistic Hedge – a common variant of multiplicative-weights-updates with recency bias – attains poly(log T) regret in multi-player general-sum games. In particular, when every player of the game uses Optimistic Hedge to iteratively update her strategy in response to the history of play so far, then after T rounds of interaction, each player experiences total regret that is poly(log T). Our bound improves, exponentially, the O(T¹ᐟ²) regret attainable by standard no-regret learners in games, the O(T¹ᐟ⁴) regret attainable by no-regret learners with recency bias [Syr+15], and the O(T¹ᐟ⁶) bound that was recently shown for Optimistic Hedge in the special case of two-player games [CP20]. A corollary of our bound is that Optimistic Hedge converges to coarse correlated equilibrium in general games at a rate of [formula].
We then extend this result from external regret to internal and swap regret, thereby establishing uncoupled learning dynamics that converge to an approximate correlated equilibrium at the rate of [formula]. This substantially improves over the prior best rate of convergence for correlated equilibria of O(T⁻³ᐟ⁴) due to Chen and Peng (NeurIPS ‘20), and it is optimal up to polylogarithmic factors in T.
The results presented here originate from my works [DFG21] and [Ana+22].
S.M.
Massachusetts Institute of Technology
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No-Regret Learning in General Games
Thesis
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Master
Master of Science in Electrical Engineering and Computer Science
Publication
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unknown
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<Abstract>This thesis investigates the regret performance of no-regret learning algorithms in the competitive, though not fully-adversarial, environment of games. We establish exponential improvements on previously best-known external and internal regret bounds for these settings.
We show that Optimistic Hedge – a common variant of multiplicative-weights-updates with recency bias – attains poly(log T) regret in multi-player general-sum games. In particular, when every player of the game uses Optimistic Hedge to iteratively update her strategy in response to the history of play so far, then after T rounds of interaction, each player experiences total regret that is poly(log T). Our bound improves, exponentially, the O(T¹ᐟ²) regret attainable by standard no-regret learners in games, the O(T¹ᐟ⁴) regret attainable by no-regret learners with recency bias [Syr+15], and the O(T¹ᐟ⁶) bound that was recently shown for Optimistic Hedge in the special case of two-player games [CP20]. A corollary of our bound is that Optimistic Hedge converges to coarse correlated equilibrium in general games at a rate of [formula].
We then extend this result from external regret to internal and swap regret, thereby establishing uncoupled learning dynamics that converge to an approximate correlated equilibrium at the rate of [formula]. This substantially improves over the prior best rate of convergence for correlated equilibria of O(T⁻³ᐟ⁴) due to Chen and Peng (NeurIPS ‘20), and it is optimal up to polylogarithmic factors in T.
The results presented here originate from my works [DFG21] and [Ana+22].</Abstract>
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