相关论文: Approachability of convex sets in generalized quit…

We provide a necessary and sufficient condition under which a convex set is approachable in a game with partial monitoring, i.e.\ where players do not observe their opponents' moves but receive random signals. This condition is an extension…

Approachability theory, introduced by Blackwell (1956), provides fundamental results on repeated games with vector-valued payoffs, and has been usefully applied since in the theory of learning in games and to learning algorithms in the…

We unify standard frameworks for approachability both in full or partial monitoring by defining a new abstract game, called the "purely informative game", where the outcome at each stage is the maximal information players can obtain,…

The notion of approachability was introduced by Blackwell [1] in the context of vector-valued repeated games. The famous Blackwell's approachability theorem prescribes a strategy for approachability, i.e., for `steering' the average cost of…

This manuscript investigates the relationship between Blackwell Approachability, a stochastic vector-valued repeated game, and minimax theory, a single-play scalar-valued scenario. First, it is established in a general setting --- one not…

We revisit Blackwell's celebrated approachability problem which considers a repeated vector-valued game between a player and an adversary. Motivated by settings in which the action set of the player or adversary (or both) is difficult to…

Blackwell's approachability (Blackwell, 1954, 1956) is a very general online learning framework where a Decision Maker obtains vector-valued outcomes, and aims at the convergence of the average outcome to a given ``target'' set. Blackwell…

In approachability with full monitoring there are two types of conditions that are known to be equivalent for convex sets: a primal and a dual condition. The primal one is of the form: a set C is approachable if and only all containing…

Blackwell approachability, regret minimization and calibration are three criteria evaluating a strategy (or an algorithm) in different sequential decision problems, or repeated games between a player and Nature. Although they have at first…

The notion of approachability in repeated games with vector payoffs was introduced by Blackwell in the 1950s, along with geometric conditions for approachability and corresponding strategies that rely on computing {\em steering directions}…

Blackwell's approachability is a framework where two players, the Decision Maker and the Environment, play a repeated game with vector-valued payoffs. The goal of the Decision Maker is to make the average payoff converge to a given set…

We study conformal inference in non-exchangeable environments through the lens of Blackwell's theory of approachability. We first recast adaptive conformal inference (ACI, Gibbs and Cand\`es, 2021) as a repeated two-player vector-valued…

In the standard setting of approachability there are two players and a target set. The players play repeatedly a known vector-valued game where the first player wants to have the average vector-valued payoff converge to the target set which…

Classic reachability games on graphs are zero-sum games, where the goal of one player, Eve, is to visit a vertex from a given target set, and that of other player, Adam, is to prevent this. Generalised reachability games, studied by…

We study approachability theory in the presence of constraints. Given a repeated game with vector payoffs, we characterize the pairs of sets (A,D) in the payoff space such that Player 1 can guarantee that the long-run average payoff…

We provide a setting and a general approach to fair online learning with stochastic sensitive and non-sensitive contexts. The setting is a repeated game between the Player and Nature, where at each stage both pick actions based on the…

Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such…

We consider the celebrated Blackwell Approachability Theorem for two-player games with vector payoffs. We show that Blackwell's result is equivalent, via efficient reductions, to the existence of "no-regret" algorithms for Online Linear…

Approachability has become a standard tool in analyzing earning algorithms in the adversarial online learning setup. We develop a variant of approachability for games where there is ambiguity in the obtained reward that belongs to a set,…

This paper reframes approachability theory within the context of population games. Thus, whilst one player aims at driving her average payoff to a predefined set, her opponent is not malevolent but rather extracted randomly from a…