arXiv subjects

Djordje Zikelic

Publications and source records attributed to Djordje Zikelic.

4 recordsLinked to original sources

arXiv2026

Solving Robust POMDPs with Omega-regular Objectives via Partially Observable Stochastic Games

Robust POMDPs (RPOMDPs) generalize classical POMDPs to the setting where exact transition probabilities are not known -- rather, they are only known to belong to some uncertainty set of values. In this work, we study the problem of solving RPOMDPs with general omega-regular objectives, which subsume a broad class of objectives such as reachability, safety, and linear temporal logic (LTL) objectives. We show that, for (s,a)-rectangular RPOMDPs with polytopic uncertainty sets, the problem of solving RPOMDPs under omega-regular objectives can be reduced to solving partially observable stochastic games (POSGs) under omega-regular objectives. Moreover, we show for the first time that reductions can be constructed in both directions, establishing the semantic equivalence between (s,a)-rectangular RPOMDPs with polytopic uncertainty sets and POSGs. This allows us to derive a range of new computational complexity results, including both upper and lower complexity bounds, on solving RPOMDPs with different omega-regular objectives. As a corollary, we also derive new computational complexity results for RMDPs.

cs.AI↗

arXiv2026

The 2026 Singapore Consensus on Global AI Safety Research Priorities

Frontier AI capabilities and autonomy are advancing rapidly. A growing number of real-world incidents make a trusted AI ecosystem essential to embracing AI with confidence. The 2026 Singapore Consensus is an outcome of the second International Scientific Exchange on AI Safety, bringing together over 100 contributors spanning 13 countries from frontier developers, government safety institutes, academia, and civil society. Building on the 2025 report, it presents a global understanding of technical AI safety research problems of top priority, now with a dedicated focus on societal resilience and on managing the risks of increasingly autonomous AI agents.

cs.CY↗

arXiv2022

Bidding Graph Games with Partially-Observable Budgets

Two-player zero-sum "graph games" are a central model, which proceeds as follows. A token is placed on a vertex of a graph, and the two players move it to produce an infinite "play", which determines the winner or payoff of the game. Traditionally, the players alternate turns in moving the token. In "bidding games", however, the players have budgets and in each turn, an auction (bidding) determines which player moves the token. So far, bidding games have only been studied as full-information games. In this work we initiate the study of partial-information bidding games: we study bidding games in which a player's initial budget is drawn from a known probability distribution. We show that while for some bidding mechanisms and objectives, it is straightforward to adapt the results from the full-information setting to the partial-information setting, for others, the analysis is significantly more challenging, requires new techniques, and gives rise to interesting results. Specifically, we study games with "mean-payoff" objectives in combination with "poorman" bidding. We construct optimal strategies for a partially-informed player who plays against a fully-informed adversary. We show that, somewhat surprisingly, the "value" under pure strategies does not necessarily exist in such games.

cs.GT↗

arXiv2013

Cinderella, quadrilaterals and conics

We study quadrilaterals inscribed and circumscribed about conics. Our research is guided by experiments in software Cinderella. We extend the known results in projective geometry of conics and show how modern mathematical software brings new ideas in pure and applied mathematics. Poncelet theorem for quadrilaterals is proved by elementary means together with Poncelet's grid property.

math.AG↗