This paper studies repetitive negotiation over the execution of an exploration process between two self-interested, fully rational agents in a full information environmentwith side payments. A key aspect of the protocolis that the exploration’s execution may interleaves ith the negotiation itself, inflicting some degradationon the exploration’s flexibility. The advantage of this form of negotiation is in enabling the agents supervising that the exploration’s execution takes place in its agreedform as negotiated. We show that in many cases, much of the computational complexity of the new protocol can be eliminated by solving an alternative negotiation scheme according to which the parties first negotiate theexploration terms as a whole and then execute it. As demonstrated in the paper, the solution characteristics of the new protocol are somehow different from thoseof legacy negotiation protocols where the execution of the agreement reached through the negotiation is completely separated from the negotiation process. Furthermore, if the agents are given the option to control some of the negotiation protocol parameters, the resulting exploration may be suboptimal. In particular we show that the increase in an agent’s expected utility in such casesis unbounded and so is the resulting decrease in the social welfare. Surprisingly, we show that further increasingone of the agents’ level of control in some of thenegotiation parameters enables bounding the resultingdecrease in the social welfare.

We introduce the Bayes-Adaptive Interactive Partially Observable Markov Decision Process (BA-IPOMDP), the first multiagent decision model that explicitly incorporates model learning. As in I-POMDPs, the BA-IPOMDP agent maintains beliefs over interactive states, which include the physical states as well as the other agents’ models. The BA-IPOMDP assumes that the state transition and observation probabilities are unknown, and augments the interactive states to include these parameters. Beliefs are maintained over this augmented interactive state space. This (necessary) state expansion exacerbates the curse of dimensionality, especially since each I-POMDP belief update is already a recursive procedure (because an agent invokes belief updates from other agents’ perspectives as part of its own belief update, in order to anticipate other agents’ actions). We extend the interactive particle filter to perform approximate belief update on BA-IPOMDPs. We present our findings on the multiagent Tiger problem.

We propose a natural model for agent failures in congestion games. In our model, each of the agents may fail to participate in the game, introducing uncertainty regarding the set of active agents. We examine how such uncertainty may change the Nash equilibria (NE) of the game. We prove that although the perturbed game induced by the failure model is not always a congestion game, it still admits at least one pure Nash equilibrium. Then, we turn to examine the effect of failures on the maximal social cost in any NE of the perturbed game. We show that in the limit case where failure probability is negligible new equilibria never emerge, and that the social cost may decrease but it never increases. For the case of non-negligible failure probabilities, we provide a full characterization of the maximal impact of failures on the social cost under worst-case equilibrium outcomes.

In cooperative games, a key question is to find a division of payoffs to coalition members in a fair manner. Nucleolus is one of such solution concepts that provides a stable solution for the grand coalition. We study the computation of the nucleolus of a number of cooperative games, including fractional matching games and fractional edge cover games on general weighted graphs, as well as vertex cover games and clique games on weighted bipartite graphs. Our results are on the positive side---we give efficient algorithms to compute the nucleolus, as well as the least core, of all of these games.

In many real-world auctions, a bidder does not know her exact value for an item, but can perform a costly deliberation to reduce her uncertainty. Relatively little is known about such deliberative environments, which are fundamentally different from classical auction environments. In this paper, we propose a new approach that allows us to leverage classical revenue-maximization results in deliberative environments. In particular, we use Myerson (1981) to construct the first non-trivial (i.e., dependent on deliberation costs) upper bound on revenue in deliberative auctions. This bound allows us to apply existing results in the classical environment to a deliberative environment. In addition, we show that in many deliberative environments the only optimal dominant-strategy mechanisms take the form of sequential posted-price auctions.

We join the goals of two giant and related fields of research in group decision-making that have historically had little contact: fair division, and efficient mechanism design with monetary payments. To do this we adopt the standard mechanism design paradigm where utility is assumed to be quasilinear and thus transferable across agents. We generalize the traditional binary criteria of envy-freeness, proportionality, and efficiency (welfare) to measures of degree that range between 0 and 1. We demonstrate that in the canonical fair division settings under any allocatively-efficient mechanism the worst-case welfare rate is 0 and disproportionality rate is 1; in other words, the worst-case results are as bad as possible. This strongly motivates an average-case analysis. We then set as the goal identification of a mechanism that achieves high welfare, low envy, and low disproportionality in expectation across a spectrum of fair division settings. We establish that the VCG mechanism is not a satisfactory candidate, but the redistribution mechanism of [Bailey, 1997; Cavallo, 2006] is.

We consider the problem of selecting fair divisions of a heterogeneous divisible good among a set of agents. Recent work (Cohler et al., AAAI 2011) focused on designing algorithms for computing maxsum—social welfare maximizing—allocations under the fairness notion of envy-freeness. Maxsum allocations can also be found under alternative notions such as equitability. In this paper, we examine the properties of these allocations. In particular, We provide conditions for when maxsum envy-free or equitable allocations are Pareto optimal and give examples where fairness with Pareto optimality is not possible. We also prove that maxsum envy-free allocations have weakly greater welfare than maxsum equitable allocations when agents have structured valuations, and we derive an approximate version of this inequality for general valuations.

We consider the classic cake cutting problem where one allocates a divisible cake to n participating agents. Among all valid divisions, fairness and efficiency (a.k.a. ~social welfare) are the most critical criteria to satisfy and optimize, respectively. We study computational complexity of computing an efficiency optimal division given the conditions that the allocation satisfies proportional fairness and assigns each agent a connected piece. For linear valuation functions, we give a polynomial time approximation scheme to compute an efficiency optimal allocation. On the other hand, we show that the problem is NP-hard to approximate within a factor of Ω 1/√ n for general piecewise constant functions, and is NP-hard to compute for normalized functions.

Many noise models do not faithfully reflect the noise processes introduced during data collection in many real-world applications. In particular, we argue that a type of noise referred to as sparse noise is quite commonly found in many applications and many existing works have been proposed to model such sparse noise. However, all the existing works only focus on unsupervised learning without considering the supervised information, i.e., label information. In this paper, we consider how to model and handle sparse noise in the context of embedding high-dimensional data under a probabilistic formulation for supervised learning. We propose a supervised probabilistic robust embedding (SPRE) model in which data are corrupted either by sparse noise or by a combination of Gaussian and sparse noises. By using the Laplace distribution as a prior to model sparse noise, we devise a two-fold variational EM learning algorithm in which the update of model parameters has analytical solution. We report some classification experiments to compare SPRE with several related models.

Kernel methods have been successfully applied to many machine learning problems. Nevertheless, since the performance of kernel methods depends heavily on the type of kernels being used, identifying good kernels among a set of given kernels is important to the success of kernel methods. A straightforward approach to address this problem is cross-validation by training a separate classifier for each kernel and choosing the best kernel classifier out of them. Another approach is Multiple Kernel Learning (MKL), which aims to learn a single kernel classifier from an optimal combination of multiple kernels. However, both approaches suffer from a high computational cost in computing the full kernel matrices and in training, especially when the number of kernels or the number of training examples is very large. In this paper, we tackle this problem by proposing an efficient online kernel selection algorithm. It incrementally learns a weight for each kernel classifier. The weight for each kernel classifier can help us to select a good kernel among a set of given kernels. The proposed approach is efficient in that (i) it is an online approach and therefore avoids computing all the full kernel matrices before training; (ii) it only updates a single kernel classifier each time by a sampling technique and therefore saves time on updating kernel classifiers with poor performance; (iii) it has a theoretically guaranteed performance compared to the best kernel predictor. Empirical studies on image classification tasks demonstrate the effectiveness of the proposed approach for selecting a good kernel among a set of kernels.