Gaggero, Mauro and Gnecco, Giorgio and Sanguineti, Marcello and Zoppoli, Riccardo Dynamic Programming And ValueFunction Approximation With Application To Optimal Consumption. In: AIRO 2012, September 4th7th, 2012, Vietri sul Mare, Italy p. 159. (2012)
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Abstract
Sequential decision problems are considered, where a reward additive over a number of stages has to be maximized. Instances arise in scheduling eets of vehicles, allocating resources, selling assets, optimizing transportation or telecommunication networks, inventory forecasting, financial planning, etc. At each stage, Dynamic Programming (DP) introduces the value function, which gives the value of the reward to be incurred at the next stage, as a function of the state at the current stage. The solution is formally obtained via recursive equations. However, closedform solutions can be derived only in particular cases. We investigate how DP and suitable approximations of the value functions can be combined, providing a methodology to face highdimensional sequential decision problems. Approximations of the value functions are considered, expressed as linear combinations of basis functions obtained from a "mother function" (e.g., the Gaussian), by varying some "inner parameters" (e.g., variance and center coordinates) [15]. The accuracies of such suboptimal solutions are estimated. It is shown that one can cope with the \curse of dimensionality" in valuefunction approximation (i.e., an exponential growth of the number of basis functions, required to guarantee a desired solution accuracy). The theoretical analysis is applied to a multidimensional version of the optimal consumption problem. (In the classical version, a consumer aims at maximizing the discounted value of the consumption of a good, given a time horizon, a sequence of interest rates, an initial wealth, and an income earned at each stage. Here, more consumers are considered.) The proposed approximation scheme is compared with classical linear approximators, i.e., linear combinations of apriori fixed basis functions. It is shown via simulations that the our approach provides a better solution accuracy, the number of computational units being the same as in fixedbasis approximation.
Item Type:  Conference or Workshop Item (Paper) 

Additional Information:  43rd Conference of the Italian Operational Research Society 
Subjects:  Q Science > QA Mathematics > QA75 Electronic computers. Computer science 
Research Area:  Computer Science and Applications 
Depositing User:  Giorgio Gnecco 
Date Deposited:  17 Sep 2013 08:12 
Last Modified:  17 Sep 2013 08:12 
URI:  http://eprints.imtlucca.it/id/eprint/1757 
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Dynamic Programming And ValueFunction Approximation With
Application To Optimal Consumption. (deposited 11 Sep 2013 10:28)
 Dynamic Programming And ValueFunction Approximation With Application To Optimal Consumption. (deposited 17 Sep 2013 08:12) [Currently Displayed]
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