arXiv subjects

Abbas Edalat

Publications and source records attributed to Abbas Edalat.

24 records · Page 2Linked to original sources

arXiv2023

A Language for Evaluating Derivatives of Functionals Using Automatic Differentiation

We present a simple functional programming language, called Dual PCF, that implements forward mode automatic differentiation using dual numbers in the framework of exact real number computation. The main new feature of this language is the ability to evaluate correctly up to the precision specified by the user -- in a simple and direct way -- the directional derivative of functionals as well as first order functions. In contrast to other comparable languages, Dual PCF also includes the recursive operator for defining functions and functionals. We provide a wide range of examples of Lipschitz functions and functionals that can be defined in Dual PCF. We use domain theory both to give a denotational semantics to the language and to prove the correctness of the new derivative operator using logical relations. To be able to differentiate functionals -- including on function spaces equipped with their compact-open topology that do not admit a norm -- we develop a domain-theoretic directional derivative that is Scott continuous and extends Clarke's subgradient of real-valued locally Lipschitz maps on Banach spaces to real-valued continuous maps on Hausdorff topological vector spaces. Finally, we show that we can express arbitrary computable linear functionals in Dual PCF.

cs.LO↗

arXiv2023

A Multilingual Virtual Guide for Self-Attachment Technique

In this work, we propose a computational framework that leverages existing out-of-language data to create a conversational agent for the delivery of Self-Attachment Technique (SAT) in Mandarin. Our framework does not require large-scale human translations, yet it achieves a comparable performance whilst also maintaining safety and reliability. We propose two different methods of augmenting available response data through empathetic rewriting. We evaluate our chatbot against a previous, English-only SAT chatbot through non-clinical human trials (N=42), each lasting five days, and quantitatively show that we are able to attain a comparable level of performance to the English SAT chatbot. We provide qualitative analysis on the limitations of our study and suggestions with the aim of guiding future improvements.

cs.CL↗

arXiv2023

Pure Bayesian Nash equilibrium for Bayesian games with multidimensional vector Types and linear payoffs

We study $n$-agent Bayesian Games with $m$-dimensional vector types and linear payoffs, also called Linear Multidimensional Bayesian Games. This class of games is equivalent with $n$-agent, $m$-game Uniform Multigames. We distinguish between games that have a discrete type space and those with a continuous type space. More specifically, we are interested in the existence of pure Bayesian Nash Equilibrium for such games and efficient algorithms to find them. For continuous priors we suggest a methodology to perform Nash Equilibrium search in simple cases. For discrete priors we present algorithms that can handle two actions and two players games efficiently. We introduce the core concept of threshold strategy and, under some mild conditions, we show that these games have at least one pure Bayesian Nash Equilibrium. We illustrate our results with several examples like Double Game Prisoner Dilemna (DGPD), Chicken Game and Sustainable Adoption Decision Problem (SADP).

cs.GT↗

arXiv2023

Recursive Solution of Initial Value Problems with Temporal Discretization

We construct a continuous domain for temporal discretization of differential equations. By using this domain, and the domain of Lipschitz maps, we formulate a generalization of the Euler operator, which exhibits second-order convergence. We prove computability of the operator within the framework of effectively given domains. The operator only requires the vector field of the differential equation to be Lipschitz continuous, in contrast to the related operators in the literature which require the vector field to be at least continuously differentiable. Within the same framework, we also analyze temporal discretization and computability of another variant of the Euler operator formulated according to Runge-Kutta theory. We prove that, compared with this variant, the second-order operator that we formulate directly, not only imposes weaker assumptions on the vector field, but also exhibits superior convergence rate. We implement the first-order, second-order, and Runge-Kutta Euler operators using arbitrary-precision interval arithmetic, and report on some experiments. The experiments confirm our theoretical results. In particular, we observe the superior convergence rate of our second-order operator compared with the Runge-Kutta Euler and the common (first-order) Euler operators.

math.NA↗

arXiv2018

Prior Independent Equilibria and Linear Multi-dimensional Bayesian Games

We show that a Bayesian strategy map profile is a Bayesian Nash Equilibrium independent of any prior if and only if the Bayesian strategy map profile, evaluated at any type profile, is the Nash equilibrium of the so-called local deterministic game corresponding to that type profile. We call such a Bayesian game type-regular. We then show that an m-dimensional n-agent Bayesian game whose utilities are linearly dependent on the types of the agents is equivalent, following a normalisation of the type space of each agent into the (m-1)-simplex, to a simultaneous competition in nm so-called basic n-agent games. If the game is own-type-linear, i.e., the utility of each player only depends linearly on its own type, then the Bayesian game is equivalent to a simultaneous competition in m basic n-agent games, called a multi-game. We then prove that an own-type-linear Bayesian game is type-regular if it is type-regular on the vertices of the (m-1)-simplex, a result which provides a large class of type-regular Bayesian maps. The class of m-dimensional own-type-linear Bayesian games can model, via their equivalence with multi-games, simultaneous decision-making in m different environments. We show that a two dimensional own-type-linear Bayesian game can be used to give a new model of the Prisoner's Dilemma (PD) in which the prosocial tendencies of the agents are considered as their types and the two agents play simultaneously in the PD as well as in a prosocial game. This Bayesian game addresses the materialistic and the prosocial tendencies of the agents. Similarly, we present a new two dimensional Bayesian model of the Trust game in which the type of the two agents reflect their prosocial tendency or trustfulness, which leads to more reasonable Nash equilibria. We finally consider an example of such multi-environment decision making in production by several companies in multi-markets.

cs.GT↗

arXiv2012

Multi-games and a double game extension of the Prisoner's Dilemma

We propose a new class of games, called Multi-Games (MG), in which a given number of players play a fixed number of basic games simultaneously. In each round of the MG, each player will have a specific set of weights, one for each basic game, which add up to one and represent the fraction of the player's investment in each basic game. The total payoff for each player is then the convex combination, with the corresponding weights, of the payoffs it obtains in the basic games. The basic games in a MG can be regarded as different environments for the players. When the players' weights for the different games in MG are private information or types with given conditional probability distributions, we obtain a particular class of Bayesian games. We show that for the class of so-called completely pure regular Double Game (DG) with finite sets of types, the Nash equilibria (NE) of the basic games can be used to compute a Bayesian Nash equilibrium of the DG in linear time with respect to the number of types of the players. We study a DG for the Prisoner's Dilemma (PD) by extending the PD with a second so-called Social Game (SG), generalising the notion of altruistic extension of a game in which players have different altruistic levels (or social coefficients). We study two different examples of Bayesian games in this context in which the social coefficients have a finite set of values and each player only knows the probability distribution of the opponent's social coefficient. In the first case we have a completely pure regular DG for which we deduce a Bayesian NE. Finally, we use the second example to compare various strategies in a round-robin tournament of the DG for PD, in which the players can change their social coefficients incrementally from one round to the next.

cs.GT↗