We introduce a natural extension of the notion of swap regret, conditional swap regret, that allows for action modifications conditioned on the player’s action history. We prove a series of new results for conditional swap regret minimization. We present algorithms for minimizing conditional swap regret with bounded conditioning history. We further extend these results to the case where conditi...

We consider regret minimization in repeated games with non-convex loss functions. Minimizing the standard notion of regret is computationally intractable. Thus, we define a natural notion of regret which permits efficient optimization and generalizes offline guarantees for convergence to an approximate local optimum. We give gradient-based methods that achieve optimal regret, which in turn guar...

Online learning algorithms that minimize regret provide strong guarantees in situations that involve repeatedly making decisions in an uncertain environment, e.g. a driver deciding what route to drive to work every day. While regret minimization has been extensively studied in repeated games, we study regret minimization for a richer class of games called bounded memory games. In each round of ...

For some well-known games, such as the Traveler’s Dilemma or the Centipede Game, traditional gametheoretic solution concepts—most notably Nash equilibrium—predict outcomes that are not consistent with empirical observations. We introduce a new solution concept, iterated regret minimization, which exhibits the same qualitative behavior as that observed in experiments in many games of interest, i...

For some well-known games, such as the Traveler’s Dilemma or the Centipede Game, traditional game-theoretic solution concepts—and most notably Nash equilibrium—predict outcomes that are not consistent with empirical observations. In this paper, we introduce a new solution concept, iterated regret minimization, which exhibits the same qualitative behavior as that observed in experiments in many ...

In two-player zero-sum games, if both players minimize their average external regret, then the average of the strategy profiles converges to a Nash equilibrium. For n-player general-sum games, however, theoretical guarantees for regret minimization are less understood. Nonetheless, Counterfactual Regret Minimization (CFR), a popular regret minimization algorithm for extensiveform games, has gen...

We price various financial instruments, which are classified as exotic options, using the regret bounds of an online algorithm. In addition, we derive a general result, which upper bounds the price of any derivative whose payoff is a convex function of the final asset price. The market model used is adversarial, making our price bounds robust. Our results extend the work of [9], which used regr...

Iterated regret minimization has been introduced recently by J.Y. Halpern and R. Pass in classical strategic games. For many games of interest, this new solution concept provides solutions that are judged more reasonable than solutions offered by traditional game concepts – such as Nash equilibrium –. In this paper, we investigate iterated regret minimization for infinite duration two-player qu...

Regret minimization has proven to be a very powerful tool in both computational learning theory and online algorithms. Regret minimization algorithms can guarantee, for a single decision maker, a near optimal behavior under fairly adversarial assumptions. I will discuss a recent extensions of the classical regret minimization model, which enable to handle many different settings related to job ...

A well studied and general setting for prediction and decision making is regret minimization in games. Recently the design of algorithms in this setting has been influenced by tools from convex optimization. In this chapter we describe the recent framework of online convex optimization which naturally merges optimization and regret minimization. We describe the basic algorithms and tools at the...