In this paper we revisit the fixed-confidence identification of the Pareto optimal set in a multi-objective multi-armed bandit model.

With our proposed method, decision-makers can simultaneously have the evaluated solutions and the approximate Pareto set.

It is desirable to obtain an approximate Pareto front with a limited evaluation budget.

We also find the optimal hyperparameters for each perturbation, which can achieve the minimax optimal regret bound with respect to total rounds.

We consider a setting in which a principal gets to choose which game from some given set is played by a group of agents. The principal would like to choose a game that favors one of the players, the social preferences of the players, or the principal's own preferences. Unfortunately, given the potential multiplicity of equilibria, it is conceptually unclear how to tell which of even any two games is better. Oesterheld et al. (2022) propose that we use assumptions about outcome correspondence -- i.e., about how the outcomes of different games relate -- to allow comparisons in some cases. For example, it seems reasonable to assume that isomorphic games are played isomorphically. From such assumptions we can sometimes deduce that the outcome of one game G' is guaranteed to be better than the outcome of another game G, even if we do not have beliefs about how each of G and G' will be played individually. Following Oesterheld et al., we then call G' a safe improvement on G. In this paper, we study how to derive safe improvement relations. We first show that if we are given a set of games and arbitrary assumptions about outcome correspondence between these games, deriving safe improvement relations is co-NP-complete. We then study the (in)completeness of a natural set of inference rules for outcome correspondence. We show that in general the inference rules are incomplete. However, we also show that under natural, generally applicable assumptions about outcome correspondence the rules are complete.

We introduce active generation of Pareto sets (A-GPS), a new framework for online discrete black-box multi-objective optimization (MOO). A-GPS learns a generative model of the Pareto set that supports a-posteriori conditioning on user preferences. The method employs a class probability estimator (CPE) to predict non-dominance relations and to condition the generative model toward high-performing regions of the search space. We also show that this non-dominance CPE implicitly estimates the probability of hypervolume improvement (PHVI). To incorporate subjective trade-offs, A-GPS introduces preference direction vectors that encode user-specified preferences in objective space. At each iteration, the model is updated using both Pareto membership and alignment with these preference directions, producing an amortized generative model capable of sampling across the Pareto front without retraining. The result is a simple yet powerful approach that achieves high-quality Pareto set approximations, avoids explicit hypervolume computation, and flexibly captures user preferences. Empirical results on synthetic benchmarks and protein design tasks demonstrate strong sample efficiency and effective preference incorporation.

The various clustering problems that have been studied intensively include, e.g., the

Negotiation is a powerful tool for modelling complex interactions between self - interested agents, which can be people, companies or increasingly, AI - enabled autonomous agents, that aim to reach the best agreement for their human owners. While negotiation is often thought as a competitive process, in which one part y wins and the other one l oses, in practice most real negotiations involve more complex, win - win scenarios ( Raif fa [20]), in which agreements can be found that maximize the utilities of both agents . S uch outcomes (agreements) are called Pareto - efficient, i.e. it is not possible to find another outcome that would increase one agent's utility, without making another agent worse off. Yet, finding agreements that are Pareto - efficient is a challenging computational problem, especially in complex negotiation domains, where issues negotiated upon are interdependent (i.e. the utility of the value chosen for one negotiation issue depends strongly on the choice for other one s). Consider, for example, the negotiations between parties in a logistic supply chain: producers want to have certain combinations of resources/quantities, delivered at certain times to be able to produce their goods, whil e suppliers may face similar constraints in their cost function for supplying different combinations of items . Or the peer - to - peer negotiations between prosumers in a decentralised power grid, that require certain amounts of energy at different times and locations, which involve non - linear constraints, especially if the capacity of the distribution network is limited .