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We introduce the pathwise optimization (PO) method, a new convex optimization procedure to produce upper and lower bounds on the optimal value (the 'price') of a high-dimensional optimal stopping problem. The PO method builds on a dual characterization of optimal stopping problems as optimization problems over the space of martingales, which we dub the(More)
In this paper we study resource allocation problems that involve multiple self-interested parties or players, and a central decision maker. We introduce and study the price of fairness, which is the relative system efficiency loss under a " fair " allocation assuming that a fully efficient allocation is one that maximizes the sum of player utilities. We(More)
This paper presents a general class of dynamic stochastic optimization problems we refer to as Stochastic Depletion Problems. A number of challenging dynamic optimization problems of practical interest are stochastic depletion problems. Optimal solutions for such problems are difficult to obtain, both from a pragmatic computational perspective as also from(More)
We visit the following fundamental problem: For a 'generic' model of consumer choice (namely, distributions over preference lists) and a limited amount of data on how consumers actually make decisions (such as marginal preference information), how may one predict revenues from offering a particular assortment of choices? This problem is central to areas(More)
We study a problem of dynamic pricing faced by a vendor with limited inventory, uncertain about demand, aiming to maximize expected discounted revenue over an infinite time horizon. The vendor learns from purchase data, so his strategy must take into account the impact of price on both revenue and future observations. We focus on a model in which customers(More)
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP naturally restrict attention to approximations that are lower bounds to the optimal cost-to-go function. Our program – the 'smoothed approximate linear program' – relaxes this(More)
—We consider an agent interacting with an unmodeled environment. At each time, the agent makes an observation, takes an action, and incurs a cost. Its actions can influence future observations and costs. The goal is to minimize the long-term average cost. We propose a novel algorithm, known as the active LZ algorithm , for optimal control based on ideas(More)
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural 'projection' of a well studied linear program for exact dynamic programming. Such programs restrict attention to approximations that are(More)
A central push in operations models over the last decade has been the incorporation of models of customer choice. Real world implementations of many of these models face the formidable stumbling block of simply identifying the 'right' model of choice to use. Thus motivated, we visit the following problem: For a 'generic' model of consumer choice (namely,(More)