Ruprecht-Karls-Universität Heidelberg
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„Detecting danger in gridworlds using Gromov's Link Condition“
Thomas Burns, Okinawa Institute of Science and Technology, Japan

Abstract: Gridworlds have been long-utilised in AI research, particularly in reinforcement learning, as they provide simple yet scalable models for many real-world applications such as robot navigation, emergent behaviour, and operations research. We initiate a study of gridworlds using the mathematical framework of reconfigurable systems and state complexes due to Abrams, Ghrist & Peterson. State complexes represent all possible configurations of a system as a single geometric space, thus making them conducive to study using geometric, topological, or combinatorial methods. The main contribution of this work is a modification to the original Abrams, Ghrist & Peterson setup which we introduce to capture agent braiding and thereby more naturally represent the topology of gridworlds. With this modification, the state complexes may exhibit geometric defects (failure of Gromov's Link Condition). Serendipitously, we discover these failures occur exactly where undesirable or dangerous states appear in the gridworld. Our results therefore provide a novel method for seeking guaranteed safety limitations in discrete task environments with single or multiple agents, and offer useful safety information (in geometric and topological forms) for incorporation in or analysis of machine learning systems. More broadly, our work introduces tools from geometric group theory and combinatorics to the AI community and demonstrates a proof-of-concept for this geometric viewpoint of the task domain through the example of simple gridworld environments.

Montag, den 26. September 2022 um 14:15 Uhr, in INF205, SR 5 Montag, den 26. September 2022 at 14:15, in INF205, SR 5

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Wienhard, Dr. Dia Taha