We consider the problem of learning in repeated games against arbitrary associates. Specifically, we study the ability of expert algorithms to quickly learn effective strategies in repeated games, towards the ultimate goal of learning near-optimal behavior against any arbitrary associate within only a handful of interactions. Our contribution is three-fold. First, we advocate a new metric, called disappointment, for evaluating expert algorithms in repeated games. Unlike minimizing traditional notions of regret, minimizing disappointment in repeated games is equivalent to maximizing payoffs. Unfortunately, eliminating disappointment is impossible to guarantee in general. However, it is possible for an expert algorithm to quickly achieve low disappointment against many known classes of algorithms in many games. Second, we show that popular existing expert algorithms often fail to achieve low disappointment against a variety of associates, particularly in early rounds of the game. Finally, we describe a new meta-algorithm that can be applied to existing expert algorithms to substantially reduce disappointment in many two-player repeated games when associates follow various static, reinforcement learning, and expert algorithms.

This paper formalizes a latent variable inference problem we call {\em supervised pattern discovery}, the goal of which is to find sets of observations that belong to a single ``pattern.'' We discuss two versions of the problem and prove uniform risk bounds for both. In the first version, collections of patterns can be generated in an arbitrary manner and the data consist of multiple labeled collections. In the second version, the patterns are assumed to be generated independently by identically distributed processes. These processes are allowed to take an arbitrary form, so observations within a pattern are not in general independent of each other. The bounds for the second version of the problem are stated in terms of a new complexity measure, the quasi-Rademacher complexity.

In this paper, we consider decentralized sequential decision making in distributed online recommender systems, where items are recommended to users based on their search query as well as their specific background including history of bought items, gender and age, all of which comprise the context information of the user. In contrast to centralized recommender systems, in which there is a single centralized seller who has access to the complete inventory of items as well as the complete record of sales and user information, in decentralized recommender systems each seller/learner only has access to the inventory of items and user information for its own products and not the products and user information of other sellers, but can get commission if it sells an item of another seller. Therefore the sellers must distributedly find out for an incoming user which items to recommend (from the set of own items or items of another seller), in order to maximize the revenue from own sales and commissions. We formulate this problem as a cooperative contextual bandit problem, analytically bound the performance of the sellers compared to the best recommendation strategy given the complete realization of user arrivals and the inventory of items, as well as the context-dependent purchase probabilities of each item, and verify our results via numerical examples on a distributed data set adapted based on Amazon data. We evaluate the dependence of the performance of a seller on the inventory of items the seller has, the number of connections it has with the other sellers, and the commissions which the seller gets by selling items of other sellers to its users.

We revisit the classical decision-theoretic problem of weighted expert voting from a statistical learning perspective. In particular, we examine the consistency (both asymptotic and finitary) of the optimal Nitzan-Paroush weighted majority and related rules. In the case of known expert competence levels, we give sharp error estimates for the optimal rule. When the competence levels are unknown, they must be empirically estimated. We provide frequentist and Bayesian analyses for this situation. Some of our proof techniques are non-standard and may be of independent interest. The bounds we derive are nearly optimal, and several challenging open problems are posed. Experimental results are provided to illustrate the theory.

Multiagent planning and coordination problems are common and known to be computationally hard. We show that a wide range of two-agent problems can be formulated as bilinear programs. We present a successive approximation algorithm that significantly outperforms the coverage set algorithm, which is the state-of-the-art method for this class of multiagent problems. Because the algorithm is formulated for bilinear programs, it is more general and simpler to implement. The new algorithm can be terminated at any time and-unlike the coverage set algorithm-it facilitates the derivation of a useful online performance bound. It is also much more efficient, on average reducing the computation time of the optimal solution by about four orders of magnitude. Finally, we introduce an automatic dimensionality reduction method that improves the effectiveness of the algorithm, extending its applicability to new domains and providing a new way to analyze a subclass of bilinear programs.

Distributed constraint optimization (DCOP) problems are a popular way of formulating and solving agent-coordination problems. A DCOP problem is a problem where several agents coordinate their values such that the sum of the resulting constraint costs is minimal. It is often desirable to solve DCOP problems with memory-bounded and asynchronous algorithms. We introduce Branch-and-Bound ADOPT (BnB-ADOPT), a memory-bounded asynchronous DCOP search algorithm that uses the message-passing and communication framework of ADOPT (Modi, Shen, Tambe, and Yokoo, 2005), a well known memory-bounded asynchronous DCOP search algorithm, but changes the search strategy of ADOPT from best-first search to depth-first branch-and-bound search. Our experimental results show that BnB-ADOPT finds cost-minimal solutions up to one order of magnitude faster than ADOPT for a variety of large DCOP problems and is as fast as NCBB, a memory-bounded synchronous DCOP search algorithm, for most of these DCOP problems. Additionally, it is often desirable to find bounded-error solutions for DCOP problems within a reasonable amount of time since finding cost-minimal solutions is NP-hard. The existing bounded-error approximation mechanism allows users only to specify an absolute error bound on the solution cost but a relative error bound is often more intuitive. Thus, we present two new bounded-error approximation mechanisms that allow for relative error bounds and implement them on top of BnB-ADOPT.

Coalition formation is a fundamental type of interaction that involves the creation of coherent groupings of distinct, autonomous, agents in order to efficiently achieve their individual or collective goals. Forming effective coalitions is a major research challenge in the field of multi-agent systems. Central to this endeavour is the problem of determining which of the many possible coalitions to form in order to achieve some goal. This usually requires calculating a value for every possible coalition, known as the coalition value, which indicates how beneficial that coalition would be if it was formed. Once these values are calculated, the agents usually need to find a combination of coalitions, in which every agent belongs to exactly one coalition, and by which the overall outcome of the system is maximized. However, this coalition structure generation problem is extremely challenging due to the number of possible solutions that need to be examined, which grows exponentially with the number of agents involved. To date, therefore, many algorithms have been proposed to solve this problem using different techniques ranging from dynamic programming, to integer programming, to stochastic search all of which suffer from major limitations relating to execution time, solution quality, and memory requirements. With this in mind, we develop an anytime algorithm to solve the coalition structure generation problem. Specifically, the algorithm uses a novel representation of the search space, which partitions the space of possible solutions into sub-spaces such that it is possible to compute upper and lower bounds on the values of the best coalition structures in them. These bounds are then used to identify the sub-spaces that have no potential of containing the optimal solution so that they can be pruned. The algorithm, then, searches through the remaining sub-spaces very efficiently using a branch-and-bound technique to avoid examining all the solutions within the searched subspace(s). In this setting, we prove that our algorithm enumerates all coalition structures efficiently by avoiding redundant and invalid solutions automatically. Moreover, in order to effectively test our algorithm we develop a new type of input distribution which allows us to generate more reliable benchmarks compared to the input distributions previously used in the field. Given this new distribution, we show that for 27 agents our algorithm is able to find solutions that are optimal in 0.175% of the time required by the fastest available algorithm in the literature. The algorithm is anytime, and if interrupted before it would have normally terminated, it can still provide a solution that is guaranteed to be within a bound from the optimal one. Moreover, the guarantees we provide on the quality of the solution are significantly better than those provided by the previous state of the art algorithms designed for this purpose. For example, for the worst case distribution given 25 agents, our algorithm is able to find a 90% efficient solution in around 10% of time it takes to find the optimal solution.

In this paper, we investigate knowledge reasoning within a simple framework called knowledge structure. We use variable forgetting as a basic operation for one agent to reason about its own or other agents\ knowledge. In our framework, two notions namely agents\ observable variables and the weakest sufficient condition play important roles in knowledge reasoning. Given a background knowledge base and a set of observable variables for each agent, we show that the notion of an agent knowing a formula can be defined as a weakest sufficient condition of the formula under background knowledge base. Moreover, we show how to capture the notion of common knowledge by using a generalized notion of weakest sufficient condition. Also, we show that public announcement operator can be conveniently dealt with via our notion of knowledge structure. Further, we explore the computational complexity of the problem whether an epistemic formula is realized in a knowledge structure. In the general case, this problem is PSPACE-hard; however, for some interesting subcases, it can be reduced to co-NP. Finally, we discuss possible applications of our framework in some interesting domains such as the automated analysis of the well-known muddy children puzzle and the verification of the revised Needham-Schroeder protocol. We believe that there are many scenarios where the natural presentation of the available information about knowledge is under the form of a knowledge structure. What makes it valuable compared with the corresponding multi-agent S5 Kripke structure is that it can be much more succinct.

We present DCL-PC: a logic for reasoning about how the abilities of agents and coalitions of agents are altered by transferring control from one agent to another. The logical foundation of DCL-PC is CL-PC, a logic for reasoning about cooperation in which the abilities of agents and coalitions of agents stem from a distribution of atomic Boolean variables to individual agents -- the choices available to a coalition correspond to assignments to the variables the coalition controls. The basic modal constructs of DCL-PC are of the form coalition C can cooperate to bring about phi. DCL-PC extends CL-PC with dynamic logic modalities in which atomic programs are of the form agent i gives control of variable p to agent j; as usual in dynamic logic, these atomic programs may be combined using sequence, iteration, choice, and test operators to form complex programs. By combining such dynamic transfer programs with cooperation modalities, it becomes possible to reason about how the power of agents and coalitions is affected by the transfer of control. We give two alternative semantics for the logic: a direct semantics, in which we capture the distributions of Boolean variables to agents; and a more conventional Kripke semantics. We prove that these semantics are equivalent, and then present an axiomatization for the logic. We investigate the computational complexity of model checking and satisfiability for DCL-PC, and show that both problems are PSPACE-complete (and hence no worse than the underlying logic CL-PC). Finally, we investigate the characterisation of control in DCL-PC. We distinguish between first-order control -- the ability of an agent or coalition to control some state of affairs through the assignment of values to the variables under the control of the agent or coalition -- and second-order control -- the ability of an agent to exert control over the control that other agents have by transferring variables to other agents. We give a logical characterisation of second-order control.

Asynchronous Partial Overlay (APO) is a search algorithm that uses cooperative mediation to solve Distributed Constraint Satisfaction Problems (DisCSPs). The algorithm partitions the search into different subproblems of the DisCSP. The original proof of completeness of the APO algorithm is based on the growth of the size of the subproblems. The present paper demonstrates that this expected growth of subproblems does not occur in some situations, leading to a termination problem of the algorithm. The problematic parts in the APO algorithm that interfere with its completeness are identified and necessary modifications to the algorithm that fix these problematic parts are given. The resulting version of the algorithm, Complete Asynchronous Partial Overlay (CompAPO), ensures its completeness. Formal proofs for the soundness and completeness of CompAPO are given. A detailed performance evaluation of CompAPO comparing it to other DisCSP algorithms is presented, along with an extensive experimental evaluation of the algorithm's unique behavior. Additionally, an optimization version of the algorithm, CompOptAPO, is presented, discussed, and evaluated.