The Limitations of Optimization from Samples

In this paper we consider the following question: can we optimize objective functions from the training data we use to learn them? We formalize this question through a novel framework we call optimization from samples (OPS). In OPS, we are given sampled values of a function drawn from some distribution and the objective is to optimize the function under some constraint. While there are interesting classes of functions that can be optimized from samples, our main result is an impossibility. We show that there are classes of functions which are statistically learnable and optimizable, but for which no reasonable approximation for optimization from samples is achievable. In particular, our main result shows that there is no constant factor approximation for maximizing coverage functions under a cardinality constraint using polynomially-many samples drawn from any distribution. We also show tight approximation guarantees for maximization under a cardinality constraint of several interesting classes of functions including unit-demand, additive, and general monotone submodular functions, as well as a constant factor approximation for monotone submodular functions with bounded curvature

COllective INtelligence with task assignment

In this paper we study the COllective INtelligence (COIN) framework of Wolpert et al. for dispersion games (Grenager, Powers and Shoham, 2002) and variants of the EL Farol Bar problem. These settings constitute difficult MAS problems where fine-grained coordination between the agents is required. We enhance the COIN framework to dramatically improve convergence results for MAS with a large number of agents. The increased convergence properties for the dispersion games are competitive with especially tailored strategies for solving dispersion games. The enhancements to the COIN framework proved to be essential to solve the more complex variants of the El Farol Bar-like problem

Methods for analyzing routing games:Information design, risk-averseness, and Braess's paradox

We study ways in which information about traffic networks can be used to achieve social objectives, such as decreasing experienced travel time. First we study how behaviour of drivers changes when the total amount of traffic changes. We give an exact characterization of this change in behaviour, which is computationally feasible to obtain. We then use insights obtained from deriving this characterization to consider the difficult problem of detecting Braess’s paradox in a network, where removal of a road leads to decreased travel time for all drivers. We give some new, efficient methods for detecting this phenomenon, and also show that in some cases the existence of Braess’s paradox in a network may be a good thing. Next we study traffic networks with potentially unpredictable travel costs. We investigate a scenario a central planner can strategically withhold information from drivers on the road to prevent congestion and benefit all road users. However, the planner’s strategy depends upon the prior beliefs about the roads that the drivers adhere to, and we study how a planner can derive these beliefs by observing the behaviour of the drivers.Finally we study the scenario where drivers are risk-averse, and can thus avoid roads that are quick on average, but can be significantly slowed in some cases