{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/150227"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/150227","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"No-Regret Learning in General Games","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_html":"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_has_math":false,"creators":["Fishelson, Maxwell K."],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science","school":null,"contributors":[],"advisors":["Daskalakis, Constantinos"],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-02","date_published":"2023-02","updated_at":"2026-07-22T22:21:28Z","subjects":[],"languages":[],"rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"rights_urls":["http://rightsstatements.org/page/InC-EDU/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/150227","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Daskalakis, Constantinos"]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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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]."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["No-Regret Learning in General Games"]}]}],"canonical_facts":{"dc:contributor.advisor":["Daskalakis, Constantinos"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["Fishelson, Maxwell K."],"dc:date.accessioned":["2023-03-31T14:41:01Z"],"dc:date.available":["2023-03-31T14:41:01Z"],"dc:date.issued":["2023-02"],"dc:description.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. 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