TY - CONF AB - Entropic risk (ERisk) is an established risk measure in finance, quantifying risk by an exponential re-weighting of rewards. We study ERisk for the first time in the context of turn-based stochastic games with the total reward objective. This gives rise to an objective function that demands the control of systems in a risk-averse manner. We show that the resulting games are determined and, in particular, admit optimal memoryless deterministic strategies. This contrasts risk measures that previously have been considered in the special case of Markov decision processes and that require randomization and/or memory. We provide several results on the decidability and the computational complexity of the threshold problem, i.e. whether the optimal value of ERisk exceeds a given threshold. In the most general case, the problem is decidable subject to Shanuel’s conjecture. If all inputs are rational, the resulting threshold problem can be solved using algebraic numbers, leading to decidability via a polynomial-time reduction to the existential theory of the reals. Further restrictions on the encoding of the input allow the solution of the threshold problem in NP∩coNP. Finally, an approximation algorithm for the optimal value of ERisk is provided. AU - Baier, Christel AU - Chatterjee, Krishnendu AU - Meggendorfer, Tobias AU - Piribauer, Jakob ID - 14417 SN - 9783959772921 T2 - 48th International Symposium on Mathematical Foundations of Computer Science TI - Entropic risk for turn-based stochastic games VL - 272 ER - TY - JOUR AB - Allometric settings of population dynamics models are appealing due to their parsimonious nature and broad utility when studying system level effects. Here, we parameterise the size-scaled Rosenzweig-MacArthur differential equations to eliminate prey-mass dependency, facilitating an in depth analytic study of the equations which incorporates scaling parameters’ contributions to coexistence. We define the functional response term to match empirical findings, and examine situations where metabolic theory derivations and observation diverge. The dynamical properties of the Rosenzweig-MacArthur system, encompassing the distribution of size-abundance equilibria, the scaling of period and amplitude of population cycling, and relationships between predator and prey abundances, are consistent with empirical observation. Our parameterisation is an accurate minimal model across 15+ orders of mass magnitude. AU - Mckerral, Jody C. AU - Kleshnina, Maria AU - Ejov, Vladimir AU - Bartle, Louise AU - Mitchell, James G. AU - Filar, Jerzy A. ID - 12706 IS - 2 JF - PLoS One TI - Empirical parameterisation and dynamical analysis of the allometric Rosenzweig-MacArthur equations VL - 18 ER - TY - CONF AB - We consider bidding games, a class of two-player zero-sum graph games. The game proceeds as follows. Both players have bounded budgets. A token is placed on a vertex of a graph, in each turn the players simultaneously submit bids, and the higher bidder moves the token, where we break bidding ties in favor of Player 1. Player 1 wins the game iff the token visits a designated target vertex. We consider, for the first time, poorman discrete-bidding in which the granularity of the bids is restricted and the higher bid is paid to the bank. Previous work either did not impose granularity restrictions or considered Richman bidding (bids are paid to the opponent). While the latter mechanisms are technically more accessible, the former is more appealing from a practical standpoint. Our study focuses on threshold budgets, which is the necessary and sufficient initial budget required for Player 1 to ensure winning against a given Player 2 budget. We first show existence of thresholds. In DAGs, we show that threshold budgets can be approximated with error bounds by thresholds under continuous-bidding and that they exhibit a periodic behavior. We identify closed-form solutions in special cases. We implement and experiment with an algorithm to find threshold budgets. AU - Avni, Guy AU - Meggendorfer, Tobias AU - Sadhukhan, Suman AU - Tkadlec, Josef AU - Zikelic, Dorde ID - 14518 SN - 0922-6389 T2 - Frontiers in Artificial Intelligence and Applications TI - Reachability poorman discrete-bidding games VL - 372 ER - TY - CONF AB - We consider the problem of learning control policies in discrete-time stochastic systems which guarantee that the system stabilizes within some specified stabilization region with probability 1. Our approach is based on the novel notion of stabilizing ranking supermartingales (sRSMs) that we introduce in this work. Our sRSMs overcome the limitation of methods proposed in previous works whose applicability is restricted to systems in which the stabilizing region cannot be left once entered under any control policy. We present a learning procedure that learns a control policy together with an sRSM that formally certifies probability 1 stability, both learned as neural networks. We show that this procedure can also be adapted to formally verifying that, under a given Lipschitz continuous control policy, the stochastic system stabilizes within some stabilizing region with probability 1. Our experimental evaluation shows that our learning procedure can successfully learn provably stabilizing policies in practice. AU - Ansaripour, Matin AU - Chatterjee, Krishnendu AU - Henzinger, Thomas A AU - Lechner, Mathias AU - Zikelic, Dorde ID - 14559 SN - 0302-9743 T2 - 21st International Symposium on Automated Technology for Verification and Analysis TI - Learning provably stabilizing neural controllers for discrete-time stochastic systems VL - 14215 ER - TY - CONF AB - We consider a natural problem dealing with weighted packet selection across a rechargeable link, which e.g., finds applications in cryptocurrency networks. The capacity of a link (u, v) is determined by how much nodes u and v allocate for this link. Specifically, the input is a finite ordered sequence of packets that arrive in both directions along a link. Given (u, v) and a packet of weight x going from u to v, node u can either accept or reject the packet. If u accepts the packet, the capacity on link (u, v) decreases by x. Correspondingly, v’s capacity on (u, v) increases by x. If a node rejects the packet, this will entail a cost affinely linear in the weight of the packet. A link is “rechargeable” in the sense that the total capacity of the link has to remain constant, but the allocation of capacity at the ends of the link can depend arbitrarily on the nodes’ decisions. The goal is to minimise the sum of the capacity injected into the link and the cost of rejecting packets. We show that the problem is NP-hard, but can be approximated efficiently with a ratio of (1+ε)⋅(1+3–√) for some arbitrary ε>0. . AU - Schmid, Stefan AU - Svoboda, Jakub AU - Yeo, Michelle X ID - 13238 SN - 0302-9743 T2 - SIROCCO 2023: Structural Information and Communication Complexity TI - Weighted packet selection for rechargeable links in cryptocurrency networks: Complexity and approximation VL - 13892 ER -