Learning in the Repeated Secretary Problem

In the classical secretary problem, one attempts to find the maximum of an unknown and unlearnable distribution through sequential search. In many real-world searches, however, distributions are not entirely unknown and can be learned through experience. To investigate learning in such a repeated secretary problem we conduct a large-scale behavioral experiment in which people search repeatedly from fixed distributions. In contrast to prior investigations that find no evidence for learning in the classical scenario, in the repeated setting we observe substantial learning resulting in near-optimal stopping behavior. We conduct a Bayesian comparison of multiple behavioral models which shows that participants' behavior is best described by a class of threshold-based models that contains the theoretically optimal strategy. Fitting such a threshold-based model to data reveals players' estimated thresholds to be surprisingly close to the optimal thresholds after only a small number of games

Self-Commitment-Institutions and Cooperation in Overlapping Generations Games

This paper focuses on a two-period OLG economy with public imperfect observability over the intergenerational cooperative dimension. Individual endowment is at free disposal and perfectly observable. In this environment we study how a new mechanism, we call Self-Commitment-Institution (SCI), outperforms personal and community enforcement in achieving higher ex-ante e¢ ciency. Social norms with and without SCI are characterized. If social norms with SCI are implemented, agents might freely dispose of their endowment. As long as they reduce their marginal gain from deviation in terms of current utility, they also credibly self-commit on intergenerational cooperation. Under quite general conditions we .nd that, even if individual strategies are still characterized by behavioral uncertainty, the introduction of SCI relaxes the inclination toward opportunistic behavior and sustains higher e¢ ciency compared to social norms without SCI. We quantify the value of SCI and investigate the role of memory with di¤erent social norms. Finally, applications on intergenerational public good games and transfer games with productive SCI are providedCooperation; Free disposal; Imperfect public monitoring; Memory; Overlapping generation game; Self-Commitment Institution;

Self-Commitment-Institutions and Cooperation in Overlapping Generations Games

This paper focuses on a two-period OLG economy with public imperfect observability over the intergenerational cooperative dimension. Individual endowment is at free disposal and perfectly observable. In this environment we study how a new mechanism, we call Self-Commitment-Institution (SCI), outperforms personal and community enforcement in achieving higher ex-ante efficiency. Social norms with and without SCI are characterized. If social norms with SCI are implemented, agents might freely dispose of their endowment. As long as they reduce their marginal gain from deviation in terms of current utility, they also credibly self-commit on intergenerational cooperation. Under quite general conditions we find that, even if individual strategies are still characterized by behavioral uncertainty, the introduction of SCI relaxes the inclination toward opportunistic behavior and sustains higher efficiency compared to social norms without SCI. We quantify the value of SCI and investigate the role of memory with different social norms. Finally, applications on intergenerational public good games and transfer games with productive SCI are provided.Cooperation, Free disposal, Imperfect public monitoring, Memory, Overlapping generation game, Self-Commitment Institution

On the Number of Iterations for Dantzig-Wolfe Optimization and Packing-Covering Approximation Algorithms

We give a lower bound on the iteration complexity of a natural class of Lagrangean-relaxation algorithms for approximately solving packing/covering linear programs. We show that, given an input with $m$ random 0/1-constraints on $n$ variables, with high probability, any such algorithm requires $\Omega(\rho \log(m)/\epsilon^2)$ iterations to compute a $(1+\epsilon)$-approximate solution, where $\rho$ is the width of the input. The bound is tight for a range of the parameters $(m,n,\rho,\epsilon)$. The algorithms in the class include Dantzig-Wolfe decomposition, Benders' decomposition, Lagrangean relaxation as developed by Held and Karp [1971] for lower-bounding TSP, and many others (e.g. by Plotkin, Shmoys, and Tardos [1988] and Grigoriadis and Khachiyan [1996]). To prove the bound, we use a discrepancy argument to show an analogous lower bound on the support size of $(1+\epsilon)$-approximate mixed strategies for random two-player zero-sum 0/1-matrix games

Channel Selection for Network-assisted D2D Communication via No-Regret Bandit Learning with Calibrated Forecasting

We consider the distributed channel selection problem in the context of device-to-device (D2D) communication as an underlay to a cellular network. Underlaid D2D users communicate directly by utilizing the cellular spectrum but their decisions are not governed by any centralized controller. Selfish D2D users that compete for access to the resources construct a distributed system, where the transmission performance depends on channel availability and quality. This information, however, is difficult to acquire. Moreover, the adverse effects of D2D users on cellular transmissions should be minimized. In order to overcome these limitations, we propose a network-assisted distributed channel selection approach in which D2D users are only allowed to use vacant cellular channels. This scenario is modeled as a multi-player multi-armed bandit game with side information, for which a distributed algorithmic solution is proposed. The solution is a combination of no-regret learning and calibrated forecasting, and can be applied to a broad class of multi-player stochastic learning problems, in addition to the formulated channel selection problem. Analytically, it is established that this approach not only yields vanishing regret (in comparison to the global optimal solution), but also guarantees that the empirical joint frequencies of the game converge to the set of correlated equilibria.Comment: 31 pages (one column), 9 figure

Improving Strategies via SMT Solving

We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number of iterations (ii) the use of merge operations (often, convex hulls) at the merge points of the control flow graph. It instead computes the least inductive invariant expressible in the domain at a restricted set of program points, and analyzes the rest of the code en bloc. We emphasize that we compute this inductive invariant precisely. For that we extend the strategy improvement algorithm of [Gawlitza and Seidl, 2007]. If we applied their method directly, we would have to solve an exponentially sized system of abstract semantic equations, resulting in memory exhaustion. Instead, we keep the system implicit and discover strategy improvements using SAT modulo real linear arithmetic (SMT). For evaluating strategies we use linear programming. Our algorithm has low polynomial space complexity and performs for contrived examples in the worst case exponentially many strategy improvement steps; this is unsurprising, since we show that the associated abstract reachability problem is Pi-p-2-complete