### 2019

Piga, Dario; Benavoli, Alessio

Semialgebraic Outer Approximations for Set-Valued Nonlinear Filtering Inproceedings

In: Proc. on European Control Conference (ECC), 2019.

Links | BibTeX | Tags: filtering, set of probabilities, SOS

@inproceedings{Piga2019,

title = {Semialgebraic Outer Approximations for Set-Valued Nonlinear Filtering},

author = {Piga, Dario and Benavoli, Alessio},

url = {http://alessiobenavoli.com/wp-content/uploads/2019/03/main_v5.pdf},

year = {2019},

date = {2019-03-24},

booktitle = {Proc. on European Control Conference (ECC)},

keywords = {filtering, set of probabilities, SOS},

pubstate = {published},

tppubtype = {inproceedings}

}

### 2017

Benavoli, Alessio; Facchini, Alessandro; Piga, Dario; Zaffalon, Marco

SOS for bounded rationality Conference

Proc. ISIPTA'17 Int. Symposium on Imprecise Probability: Theories and Applications, , PJMLR, 2017.

Abstract | Links | BibTeX | Tags: bounded rationality, SOS

@conference{Benavoli2017b,

title = {SOS for bounded rationality},

author = { Benavoli, Alessio and Facchini, Alessandro and Piga, Dario and Zaffalon, Marco},

url = {https://arxiv.org/abs/1705.02663},

year = {2017},

date = {2017-05-07},

booktitle = {Proc. ISIPTA'17 Int. Symposium on Imprecise Probability: Theories and Applications, },

pages = {1--12},

publisher = {PJMLR},

abstract = {In the gambling foundation of probability theory, rationality requires that a subject should always

(never) find desirable all nonnegative (negative) gambles, because no matter the result of the exper-

iment the subject never (always) decreases her money. Evaluating the nonnegativity of a gamble in

infinite spaces is a difficult task. In fact, even if we restrict the gambles to be polynomials in R n , the

problem of determining nonnegativity is NP-hard. The aim of this paper is to develop a computable

theory of desirable gambles. Instead of requiring the subject to accept all nonnegative gambles, we

only require her to accept gambles for which she can efficiently determine the nonnegativity (in

particular SOS polynomials). We call this new criterion bounded rationality.},

keywords = {bounded rationality, SOS},

pubstate = {published},

tppubtype = {conference}

}

In the gambling foundation of probability theory, rationality requires that a subject should always

(never) find desirable all nonnegative (negative) gambles, because no matter the result of the exper-

iment the subject never (always) decreases her money. Evaluating the nonnegativity of a gamble in

infinite spaces is a difficult task. In fact, even if we restrict the gambles to be polynomials in R n , the

problem of determining nonnegativity is NP-hard. The aim of this paper is to develop a computable

theory of desirable gambles. Instead of requiring the subject to accept all nonnegative gambles, we

only require her to accept gambles for which she can efficiently determine the nonnegativity (in

particular SOS polynomials). We call this new criterion bounded rationality.

(never) find desirable all nonnegative (negative) gambles, because no matter the result of the exper-

iment the subject never (always) decreases her money. Evaluating the nonnegativity of a gamble in

infinite spaces is a difficult task. In fact, even if we restrict the gambles to be polynomials in R n , the

problem of determining nonnegativity is NP-hard. The aim of this paper is to develop a computable

theory of desirable gambles. Instead of requiring the subject to accept all nonnegative gambles, we

only require her to accept gambles for which she can efficiently determine the nonnegativity (in

particular SOS polynomials). We call this new criterion bounded rationality.