TY  - CONF
TI  - Dynamic Programming And Value-Function Approximation With
Application To Optimal Consumption
A1  - Gnecco, Giorgio
A1  - Gaggero, Mauro
A1  - Sanguineti, Marcello
A1  - Zoppoli, Riccardo
AV  - none
N2  - 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, closed-form 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 high-dimensional 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) [1-5]. The accuracies of such suboptimal solutions are estimated. It is shown that
one can cope with the \curse of dimensionality" in value-function 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 a-priori
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 fixed-basis approximation.
M2  - Vietri sul Mare, Italy
N1  - 43rd Conference of the Italian Operational Research Society
T2  - AIRO 2012
ID  - eprints1676
UR  - http://eprints.imtlucca.it/1676/
Y1  - 2012/09//
ER  -