The Frontiers conference was a one day meeting of leading minds in Economics and Numerical Computation. The conference provided a place for economists to make connections with numerical analysts and learn state of the art computational methods.
| 9:00 am | Kenneth Judd |
| 10:15 am | Break |
| 10:30 am | Daniela P. De Farias |
| 12:00 pm | Lunch |
| 2:00 pm | Ridgway Scott |
| 3:15 pm | Break |
| 3:30 pm | Julia Tsai |
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Statistical Modeling in Solving Continuous-State
Stochastic Dynamic Programming
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[slides]
Julia Tsai, Purdue |
| In stochastic dynamic programming (SDP) with continuous state variables, the optimal (cost-to-go) value function is computed at discrete points in the state space. In this talk, an approach employing statistical methods of modeling and experimental design is described to overcome this "curse of dimensionality." The development of a parallel version of multivariate adaptive regression splines (MARS) improves the computational performance for the OA/MARS stochastic dynamic programming method. In addition, an automatic way of determining a difficult-to-select MARS parameter is developed. To cope with the tendency of high-order interaction of a MARS model, an approach that provides an alternative to lower the order of interaction is presented. |
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The Linear Programming Approach to Approximate
Dynamic Programming.
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[slides]
Daniela P. De Farias, MIT |
| Real-world problems of sequential decision making often involve complexstochastic systems. Severely nonlinear dynamics and large state andaction spaces make analysis of such systems and design of optimalpolicies difficult. Dynamic programming is a methodology for computinglong-run optimal policies. However, dynamic programming iscomputationally infeasible for systems with large state and actionspaces, a problem known as the "curse of dimensionality." Approximatedynamic programming aims to alleviate the curse of dimensionality byusing problem-specific information to efficiently approximate dynamicprogramming solutions. The focus of this talk is on the approximatedynamic programming algorithm known as approximate linear programming.I will present my recent analysis of approximate linear programming.The analysis characterizes how well the algorithm is expected toperform and identifies certain structures often observed in real-worldapplications that facilitate the design of a good policy. The analysisplaces approximate linear programming at advantage relative to otherapproximate dynamic programming methods: relatively deep understandingof the algorithm makes its implementation more streamlined, increasingthe probability of success with a reduced amount of trial and error. Applications ofapproximate linear programming to queueing problems will be discussed, illustratingpractical aspects of the methodology and its competitiveness relative to other approaches to such problems. |
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Perturbation methods for dynamic, stochastic economic models
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[paper 1] [paper 2]
Kenneth Judd,Stanford University |
| We describe a general Taylor series method for computing asymptotically valid approximations to deterministic and stochastic rational expectations models near the deterministic steady state. Contrary to conventional wisdom, the higher-order terms are conceptually easier to compute than the conventional deterministic linear approximations. We display the solvability conditions for second- and third-order approximations and show how to compute the solvability conditions in general. We provide examples where perturbation methods will fail, and use implicit function theorems to derive sufficient conditions that justify the perturbation approach. We describe an algorithm which computes the order k Taylor series expansion along with diagnostic indices indicating the quality of the approximation. We apply this algorithm to several multidimensional stochastic dynamic programming problems and show that the resulting nonlinear approximations are far superior to linear approximations. We also discuss recent advances utilizing Sylvester equation formulations, automatic differentiation, and change of variables techniques that will improve performance. |
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Numerical solution of transport and hedonic problems
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related notes:
[1]
[2]
Ridgway Scott,University of Chicago |
| We will discuss ways to solve numerically the classic Monge-Kantorovich transport problem. We show how this requires the solution of complex partial differential equations. We will describe briefly how software to do this can be produced automatically, and we show how this is being carried out in the FEniCS project (see FEniCS.org for more information). Implications for hedonic models will be presented. |