First, it is established that the setting of weak learnability aids the entire class, granting a rate O(ln(1/)). Next, the (disjoint) conditions under which the infimal empirical risk is attainable are characterized in terms of the sample and weak learning class, and a new proof is given for the known rate O(ln(1/)). Finally, it is established that any instance can be decomposed into two smaller instances resembling the two preceding special cases, yielding a rate O(1/), with a matching lower bound for the logistic loss. The principal technical hurdle throughout this work is the potential unattainability of the infimal empirical risk; the technique for overcoming this barrier may be of general interest.

In many real world situations, collective decisions are made using voting and, in scenarios such as committee or board elections, employing voting rules that return multiple winners. In multi-winner approval voting (AV), an agent submits a ballot consisting of approvals for as many candidates as they wish, and winners are chosen by tallying up the votes and choosing the top-$k$ candidates receiving the most approvals. In many scenarios, an agent may manipulate the ballot they submit in order to achieve a better outcome by voting in a way that does not reflect their true preferences. In complex and uncertain situations, agents may use heuristics instead of incurring the additional effort required to compute the manipulation which most favors them. In this paper, we examine voting behavior in single-winner and multi-winner approval voting scenarios with varying degrees of uncertainty using behavioral data obtained from Mechanical Turk. We find that people generally manipulate their vote to obtain a better outcome, but often do not identify the optimal manipulation. There are a number of predictive models of agent behavior in the COMSOC and psychology literature that are based on cognitively plausible heuristic strategies. We show that the existing approaches do not adequately model real-world data. We propose a novel model that takes into account the size of the winning set and human cognitive constraints, and demonstrate that this model is more effective at capturing real-world behaviors in multi-winner approval voting scenarios.

R.M.BURSTALL 373 23 Assertions: programs written without specifying unnecessary order.

In this paper, we aim at evaluating the impact of the starting point of a basic local search based on the first improvement strategy. We define the coverage rate of a configuration as the proportion of the search space from which a particular configuration can be reached by a strict hill-climbling with a non-zero probability. In particular, we compute the coverage rate of fitness landscapes global optima, in order to evaluate their attainability by hill-climbing algorithms. The experimental study is realized on NK landscapes, in which the size and ruggedness can be controlled. Results indicate that the coverage rate of global optima is usually high, which means that a basic strictly improving hill-climbing with first improvement strategy is able to reach global optima, independently to the starting point considered. This confirms that it is more important to focus on an effective search strategy rather than worrying about the choice of the initial configurations.

This manuscript considers the convergence rate of boosting under a large class of losses, including the exponential and logistic losses, where the best previous rate of convergence was O(exp(1/ε²)). First, it is established that the setting of weak learnability aids the entire class, granting a rate O(ln(1/ε)). Next, the (disjoint) conditions under which the infimal empirical risk is attainable are characterized in terms of the sample and weak learning class, and a new proof is given for the known rate O(ln(1/ε)). Finally, it is established that any instance can be decomposed into two smaller instances resembling the two preceding special cases, yielding a rate O(1/ε), with a matching lower bound for the logistic loss. The principal technical hurdle throughout this work is the potential unattainability of the infimal empirical risk; the technique for overcoming this barrier may be of general interest.