arXiv subjects

M. Veloso

Publications and source records attributed to M. Veloso.

3 recordsLinked to original sources

arXiv2026

On Locally Finite Derivations in Ore Extensions

Let $\Bbbk$ be an algebraically closed field of characteristic zero. We classify the locally finite derivations of arbitrary Ore extensions of $\Bbbk[x]$, thus extending van den Essen's \cite{V92} classification for the polynomial algebra $\Bbbk[x,y]$ to this noncommutative setting. More precisely, we consider the three families arising in the classification of Ore extensions of $\Bbbk[x]$: the quantum plane, the first quantum Weyl algebra, and the differential Ore extensions \[ A_h=\Bbbk[x][t;h(x)\partial_x]. \] For both the quantum plane and the first quantum Weyl algebra, we determine the locally finite derivations and explain how the resulting classifications are related to the work of Su\'arez-Alvarez and Vivas \cite{SuarezVivas} on generalized Weyl algebras. For the algebras $A_h$, with $h$ nonconstant, we obtain a complete classification in both the square-free and non-square-free cases. As a consequence, we show that $\LFD(A_h)$ is a solvable and weakly locally finite Lie subalgebra of $\Der(A_h)$, although it is not locally finite as a set of derivations.

math.RA↗

arXiv2011

Existence of Multiagent Equilibria with Limited Agents

Multiagent learning is a necessary yet challenging problem as multiagent systems become more prevalent and environments become more dynamic. Much of the groundbreaking work in this area draws on notable results from game theory, in particular, the concept of Nash equilibria. Learners that directly learn an equilibrium obviously rely on their existence. Learners that instead seek to play optimally with respect to the other players also depend upon equilibria since equilibria are fixed points for learning. From another perspective, agents with limitations are real and common. These may be undesired physical limitations as well as self-imposed rational limitations, such as abstraction and approximation techniques, used to make learning tractable. This article explores the interactions of these two important concepts: equilibria and limitations in learning. We introduce the question of whether equilibria continue to exist when agents have limitations. We look at the general effects limitations can have on agent behavior, and define a natural extension of equilibria that accounts for these limitations. Using this formalization, we make three major contributions: (i) a counterexample for the general existence of equilibria with limitations, (ii) sufficient conditions on limitations that preserve their existence, (iii) three general classes of games and limitations that satisfy these conditions. We then present empirical results from a specific multiagent learning algorithm applied to a specific instance of limited agents. These results demonstrate that learning with limitations is feasible, when the conditions outlined by our theoretical analysis hold.

cs.MA↗

arXiv1995

FLECS: Planning with a Flexible Commitment Strategy

There has been evidence that least-commitment planners can efficiently handle planning problems that involve difficult goal interactions. This evidence has led to the common belief that delayed-commitment is the "best" possible planning strategy. However, we recently found evidence that eager-commitment planners can handle a variety of planning problems more efficiently, in particular those with difficult operator choices. Resigned to the futility of trying to find a universally successful planning strategy, we devised a planner that can be used to study which domains and problems are best for which planning strategies. In this article we introduce this new planning algorithm, FLECS, which uses a FLExible Commitment Strategy with respect to plan-step orderings. It is able to use any strategy from delayed-commitment to eager-commitment. The combination of delayed and eager operator-ordering commitments allows FLECS to take advantage of the benefits of explicitly using a simulated execution state and reasoning about planning constraints. FLECS can vary its commitment strategy across different problems and domains, and also during the course of a single planning problem. FLECS represents a novel contribution to planning in that it explicitly provides the choice of which commitment strategy to use while planning. FLECS provides a framework to investigate the mapping from planning domains and problems to efficient planning strategies.

cs.AI↗