mlsanityData to 7 Oct 2026

Strategizing against No-regret Learners

arXiv 1909.13861 ↗First posted 30 Sep 2019cs.GT cs.LGcited by 48

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Abstract (arXiv)

How should a player who repeatedly plays a game against a no-regret learner strategize to maximize his utility? We study this question and show that under some mild assumptions, the player can always guarantee himself a utility of at least what he would get in a Stackelberg equilibrium of the game. When the no-regret learner has only two actions, we show that the player cannot get any higher utility than the Stackelberg equilibrium utility. But when the no-regret learner has more than two actions and plays a mean-based no-regret strategy, we show that the player can get strictly higher than the Stackelberg equilibrium utility. We provide a characterization of the optimal game-play for the player against a mean-based no-regret learner as a solution to a control problem. When the no-regret learner's strategy also guarantees him a no-swap regret, we show that the player cannot get anything higher than a Stackelberg equilibrium utility.

Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Sep 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 4; 2023: 8; 2024: 17; 2025: 11; 2026: 6.

48 papers.

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  1. 2023U-Calibration: Forecasting for an Unknown Agentcited by 46
  2. 2022Strategizing against Learners in Bayesian Gamescited by 33
  3. 2023Fast swap regret minimization and applications to approximate correlated equilibriacited by 30
  4. 2023Calibrated Stackelberg Games: Learning Optimal Commitments Against Calibrated Agentscited by 25
  5. 2021Auctions Between Regret-Minimizing Agentscited by 22
  6. 2024Contracting with a Learning Agentcited by 22
  7. 2023Is Learning in Games Good for the Learners?cited by 19
  8. 2021How and Why to Manipulate Your Own Agent: On the Incentives of Users of Learning Agentscited by 17
  9. 2025Full Swap Regret and Discretized Calibrationcited by 13
  10. 2022Diversified Recommendations for Agents with Adaptive Preferencescited by 9
  11. 2024Strategizing against No-Regret Learners in First-Price Auctionscited by 8
  12. 2023Persuading a Behavioral Agent: Approximately Best Responding and Learningcited by 7
36 more
  1. 2024Strategically-Robust Learning Algorithms for Bidding in First-Price Auctionscited by 7
  2. 2024Maximizing utility in multi-agent environments by anticipating the behavior of other learnerscited by 7
  3. 2025Swap Regret and Correlated Equilibria Beyond Normal-Form Gamescited by 7
  4. 2023Adversarial Attacks on Adversarial Banditscited by 6
  5. 2024Algorithmic Collusion Without Threatscited by 6
  6. 2025Nearly-Optimal Bandit Learning in Stackelberg Games with Side Informationcited by 6
  7. 2024Generalized Principal-Agent Problem with a Learning Agentcited by 5
  8. 2024Impact of Decentralized Learning on Player Utilities in Stackelberg Gamescited by 5
  9. 2024Is Knowledge Power? On the (Im)possibility of Learning from Strategic Interactionscited by 5
  10. 2025Should Decision-Makers Reveal Classifiers in Online Strategic Classification?cited by 5
  11. 2024Rate-Preserving Reductions for Blackwell Approachabilitycited by 4
  12. 2024Games with Payments between Learning Agentscited by 3
  13. 2024Learning to Play Against Unknown Opponentscited by 3
  14. 2025Learning and Computation of Phi-Equilibria at the Frontier of Tractabilitycited by 3
  15. 2024Learning to Steer Markovian Agents under Model Uncertaintycited by 2
  16. 2025Computational Intractability of Strategizing against Online Learnerscited by 2
  17. 2025Online Omniprediction with Long-Term Constraintscited by 2
  18. 2026Swap Regret Minimization Through Response-Based Approachabilitycited by 2
  19. 2026Near-optimal Swap Regret Minimization for Convex Lossescited by 2
  20. 2022Playing against no-regret playerscited by 1
  21. 2024Strategizing against Q-learners: A Control-theoretical Approachcited by 1
  22. 2024Online Stackelberg Optimization via Nonlinear Controlcited by 1
  23. 2024Model Selection for Average Reward RL with Application to Utility Maximization in Repeated Gamescited by 1
  24. 2025Best of Both Worlds: Regret Minimization versus Minimax Playcited by 1
  25. 2025Steering No-Regret Agents in MFGs under Model Uncertaintycited by 1
  26. 2025Proximal Regret and Proximal Correlated Equilibria: A New Tractable Solution Concept for Online Learning and Gamescited by 1
  27. 2026From No-Regret to Strategically Robust Learning in Repeated Auctionscited by 1
  28. 2022Online Learning in Supply-Chain Gamescited by 0
  29. 2023Decentralized Online Bandit Optimization on Directed Graphs with Regret Boundscited by 0
  30. 2023Achieving Better Regret against Strategic Adversariescited by 0
  31. 2024On the Complexity of Learning to Cooperate with Populations of Socially Rational Agentscited by 0
  32. 2024ReLExS: Reinforcement Learning Explanations for Stackelberg No-Regret Learnerscited by 0
  33. 2025Learning Local Stackelberg Equilibria from Repeated Interactions with a Learning Agentcited by 0
  34. 2026Learning Safely Without Knowing the World:COMPASS-Hedgecited by 0
  35. 2026Minimax-Optimal Policy Regret in Partially Observable Markov Gamescited by 0
  36. 2026Mean-based algorithms: A lower bound and regretcited by 0