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)
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 propose consensus propagation, an asynchronous distributed protocol for averaging numbers across a network. We establish convergence, characterize the convergence rate for regular graphs, and demonstrate that the protocol exhibits better scaling properties than pairwise averaging, an alternative that has received much recent attention. Consensus… (More)
SUMMARY The Pfaat protein family alignment annotation tool is a Java-based multiple sequence alignment editor and viewer designed for protein family analysis. The application merges display features such as dendrograms, secondary and tertiary protein structure with SRS retrieval, subgroup comparison, and extensive user-annotation capabilities. … (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)
We establish that the min-sum message-passing algorithm and its asynchronous variants converge for a large class of unconstrained convex optimization problems.
Systemic risk is an issue of great concern in modern financial markets as well as, more broadly, in the management of complex systems. We propose an axiomatic framework for systemic risk. Our framework allows for an independent specification of (1) a functional of the cross-sectional profile of outcomes across agents in the system in a single scenario of… (More)
—We establish the convergence of the min-sum message passing algorithm for minimization of a quadratic objective function given a convex decomposition. Our results also apply to the equivalent problem of the convergence of Gaussian belief propagation.
We develop a protocol for optimizing dynamic behavior of a network of simple electronic components, such as a sensor network, an ad hoc network of mobile devices, or a network of communication switches. This protocol requires only local communication and simple computations which are distributed among devices. The protocol is scalable to large networks. As… (More)