General self-motivation and strategy identification : Case studies based on Sokoban and Pac-Man

(c) 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, we use empowerment, a recently introduced biologically inspired measure, to allow an AI player to assign utility values to potential future states within a previously unencountered game without requiring explicit specification of goal states. We further introduce strategic affinity, a method of grouping action sequences together to form "strategies," by examining the overlap in the sets of potential future states following each such action sequence. We also demonstrate an information-theoretic method of predicting future utility. Combining these methods, we extend empowerment to soft-horizon empowerment which enables the player to select a repertoire of action sequences that aim to maintain anticipated utility. We show how this method provides a proto-heuristic for nonterminal states prior to specifying concrete game goals, and propose it as a principled candidate model for "intuitive" strategy selection, in line with other recent work on "self-motivated agent behavior." We demonstrate that the technique, despite being generically defined independently of scenario, performs quite well in relatively disparate scenarios, such as a Sokoban-inspired box-pushing scenario and in a Pac-Man-inspired predator game, suggesting novel and principle-based candidate routes toward more general game-playing algorithms.Peer reviewedFinal Accepted Versio

Hypertoric category O

We study the representation theory of the invariant subalgebra of the Weyl algebra under a torus action, which we call a "hypertoric enveloping algebra." We define an analogue of BGG category O for this algebra, and identify it with a certain category of sheaves on a hypertoric variety. We prove that a regular block of this category is highest weight and Koszul, identify its Koszul dual, compute its center, and study its cell structure. We also consider a collection of derived auto-equivalences analogous to the shuffling and twisting functors for BGG category O.Comment: 65 pages, TikZ figures (PDF is recommended; DVI will not display correctly on all computers); v3: switched terminology for twisting and shuffling; final version; v4: small correction in definition of standard module

Necessary skills and practices required for effective participation in high bandwidth design team activities

Technology is continually changing, and evolving, throughout the entire construction industry; and particularly in the design process. One of the principal manifestations of this is a move away from team working in a shared work space to team working in a virtual space, using increasingly sophisticated electronic media. Due to the significant operating differences when working in shared and virtual spaces adjustments to generic skills utilised by members is a necessity when moving between the two conditions. This paper reports an aspect of a CRC-CI research project based on research of ‘generic skills’ used by individuals and teams when engaging with high bandwidth information and communication technologies (ICT). It aligns with the project’s other two aspects of collaboration in virtual environments: ‘processes’ and ‘models’. The entire project focuses on the early stages of a project (i.e. design) in which models for the project are being developed and revised. The paper summarises the first stage of the research project which reviews literature to identify factors of virtual teaming which may affect team member skills. It concludes that design team participants require ‘appropriate skills’ to function efficiently and effectively, and that the introduction of high band-width technologies reinforces the need for skills mapping and measurement

Gale duality and Koszul duality

Given an affine hyperplane arrangement with some additional structure, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul dual to each other, and that the roles of the two algebras are reversed by Gale duality. We also study the centers and representation categories of our algebras, which are in many ways analogous to integral blocks of category O.Comment: 55 pages; v2 contains significant revisions to proofs and to some of the results. Section 7 has been deleted; that material will be incorporated into a later paper by the same author

Self-Motivated Composition of Strategic Action Policies

In the last 50 years computers have made dramatic progress in their capabilities, but at the same time their failings have demonstrated that we, as designers, do not yet understand the nature of intelligence. Chess playing, for example, was long offered up as an example of the unassailability of the human mind to Artificial Intelligence, but now a chess engine on a smartphone can beat a grandmaster. Yet, at the same time, computers struggle to beat amateur players in simpler games, such as Stratego, where sheer processing power cannot substitute for a lack of deeper understanding. The task of developing that deeper understanding is overwhelming, and has previously been underestimated. There are many threads and all must be investigated. This dissertation explores one of those threads, namely asking the question “How might an artificial agent decide on a sensible course of action, without being told what to do?”. To this end, this research builds upon empowerment, a universal utility which provides an entirely general method for allowing an agent to measure the preferability of one state over another. Empowerment requires no explicit goals, and instead favours states that maximise an agent’s control over its environment. Several extensions to the empowerment framework are proposed, which drastically increase the array of scenarios to which it can be applied, and allow it to evaluate actions in addition to states. These extensions are motivated by concepts such as bounded rationality, sub-goals, and anticipated future utility. In addition, the novel concept of strategic affinity is proposed as a general method for measuring the strategic similarity between two (or more) potential sequences of actions. It does this in a general fashion, by examining how similar the distribution of future possible states would be in the case of enacting either sequence. This allows an agent to group action sequences, even in an unknown task space, into ‘strategies’. Strategic affinity is combined with the empowerment extensions to form soft-horizon empowerment, which is capable of composing action policies in a variety of unknown scenarios. A Pac-Man-inspired prey game and the Gambler’s Problem are used to demonstrate this selfmotivated action selection, and a Sokoban inspired box-pushing scenario is used to highlight the capability to pick strategically diverse actions. The culmination of this is that soft-horizon empowerment demonstrates a variety of ‘intuitive’ behaviours, which are not dissimilar to what we might expect a human to try. This line of thinking demonstrates compelling results, and it is suggested there are a couple of avenues for immediate further research. One of the most promising of these would be applying the self-motivated methodology and strategic affinity method to a wider range of scenarios, with a view to developing improved heuristic approximations that generate similar results. A goal of replicating similar results, whilst reducing the computational overhead, could help drive an improved understanding of how we may get closer to replicating a human-like approach

Localization algebras and deformations of Koszul algebras

We show that the center of a flat graded deformation of a standard Koszul algebra behaves in many ways like the torus-equivariant cohomology ring of an algebraic variety with finite fixed-point set. In particular, the center acts by characters on the deformed standard modules, providing a "localization map." We construct a universal graded deformation, and show that the spectrum of its center is supported on a certain arrangement of hyperplanes which is orthogonal to the arrangement coming the Koszul dual algebra. This is an algebraic version of a duality discovered by Goresky and MacPherson between the equivariant cohomology rings of partial flag varieties and Springer fibers; we recover and generalize their result by showing that the center of the universal deformation for the ring governing a block of parabolic category $\mathcal{O}$ for $\mathfrak{gl}_n$ is isomorphic to the equivariant cohomology of a Spaltenstein variety. We also identify the center of the deformed version of the "category $\mathcal{O}$" of a hyperplane arrangement (defined by the authors in a previous paper) with the equivariant cohomology of a hypertoric variety.Comment: 39 pages; v3: final versio