Reducing Optimism Bias in Incomplete Cooperative Games

Cooperative game theory has diverse applications in contemporary artificial intelligence, including domains like interpretable machine learning, resource allocation, and collaborative decision-making. However, specifying a cooperative game entails assigning values to exponentially many coalitions, and obtaining even a single value can be resource-intensive in practice. Yet simply leaving certain coalition values undisclosed introduces ambiguity regarding individual contributions to the collective grand coalition. This ambiguity often leads to players holding overly optimistic expectations, stemming from either inherent biases or strategic considerations, frequently resulting in collective claims exceeding the actual grand coalition value. In this paper, we present a framework aimed at optimizing the sequence for revealing coalition values, with the overarching goal of efficiently closing the gap between players' expectations and achievable outcomes in cooperative games. Our contributions are threefold: (i) we study the individual players' optimistic completions of games with missing coalition values along with the arising gap, and investigate its analytical characteristics that facilitate more efficient optimization; (ii) we develop methods to minimize this gap over classes of games with a known prior by disclosing values of additional coalitions in both offline and online fashion; and (iii) we empirically demonstrate the algorithms' performance in practical scenarios, together with an investigation into the typical order of revealing coalition values.Comment: Proc. of the 23rd International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2024

Porovnání Brillových vln s poli singulárních prstenců

Circular matter rings are a natural zero approximation of stationary and axially symmetric structures which appear in astrophysics. If the rings are infinitesimally thin (line sources), they are singular, which in the general relativistic description typically implies weird deformation of space in their vicinity. In particular, and contrary to the Newtonian picture, such rings even tend to behave in a strongly directional manner. One solution is to consider non-singular, extended sources (toroids), which may however be difficult to treat exactly and/or be unsatisfactory in other respects. In this thesis we check another option, namely to abandon the "real matter" completely and consider a non-singular source represented by mere curvature arranged, at least at some instant, in a pattern possessing the above symmetries. One such solution of Einstein's equations is known as the Brill waves; we study its properties at the moment of time symmetry (when it is momentarily static), in order to compare it with the space-times of matter rings. 1Tenké, hmotné prstence jsou první přirozenou aproximací osově symetrických astrofyzikálních objektů. Pokud jsou prstence nekonečně tenké (neboli tvoří "čárový zdroj"), pak jsou singulární, což v obecné rel- ativitě často naznačuje zvláštní deformaci prostoru v okolí samotného prstence. Na rozdíl od klasického (Newtonovského) případu se tato řešení často chovají "směrově", tj. jejich vlastnosti závisí na směru, ze kterého je prstenec pozorován. Jedním řešením je uvažovat objemový zdroj tvaru toru. Tuto úlohu je ovšem obtížné vyřešit přesně, nebo je nevhodná v jiných ohledech. V této práci jsme prověřili jinou možnost - zcela jsme opustili hmotné zdroje a nahradili je nesingulárním zdrojem reprezentovaným pouhým zakřivením prostoročasu, který vykazuje symetrie původního řešení. Jedním takovým řešením Einsteinových rovnic jsou takzvané Brillovy vlny, které jsme studovali v okamžiku časové symetrie, abychom porovnali vlastnosti obou prostoročasů. 1Ústav teoretické fyzikyInstitute of Theoretical PhysicsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Learning not to Regret

The literature on game-theoretic equilibrium finding predominantly focuses on single games or their repeated play. Nevertheless, numerous real-world scenarios feature playing a game sampled from a distribution of similar, but not identical games, such as playing poker with different public cards or trading correlated assets on the stock market. As these similar games feature similar equilibra, we investigate a way to accelerate equilibrium finding on such a distribution. We present a novel "learning not to regret" framework, enabling us to meta-learn a regret minimizer tailored to a specific distribution. Our key contribution, Neural Predictive Regret Matching, is uniquely meta-learned to converge rapidly for the chosen distribution of games, while having regret minimization guarantees on any game. We validated our algorithms' faster convergence on a distribution of river poker games. Our experiments show that the meta-learned algorithms outpace their non-meta-learned counterparts, achieving more than tenfold improvements

Raman spectroscopic detection of the T-HgII-T base pair and the ionic characteristics of mercury

Developing applications for metal-mediated base pairs (metallo-base-pair) has recently become a high-priority area in nucleic acid research, and physicochemical analyses are important for designing and fine-tuning molecular devices using metallo-base-pairs. In this study, we characterized the HgII-mediated T-T (T-HgII-T) base pair by Raman spectroscopy, which revealed the unique physical and chemical properties of HgII. A characteristic Raman marker band at 1586 cm−1 was observed and assigned to the C4=O4 stretching mode. We confirmed the assignment by the isotopic shift (18O-labeling at O4) and density functional theory (DFT) calculations. The unusually low wavenumber of the C4=O4 stretching suggested that the bond order of the C4=O4 bond reduced from its canonical value. This reduction of the bond order can be explained if the enolate-like structure (N3=C4-O4−) is involved as a resonance contributor in the thymine ring of the T-HgII-T pair. This resonance includes the N-HgII-bonded state (HgII-N3-C4=O4) and the N-HgII-dissociated state (HgII+ N3=C4-O4−), and the latter contributor reduced the bond order of N-HgII. Consequently, the HgII nucleus in the T-HgII-T pair exhibited a cationic character. Natural bond orbital (NBO) analysis supports the interpretations of the Raman experiments

Study of geodesic chaos by fractal methods

We study the dynamics of free test particles in a field of Schwarzschild black hole surrounded by an external exact thin axisymmetric solutions of Einstein's equations. Specifically, we use the Bach-Weyl ring and two member of the inverted Morgan-Morgan family of solutions as the additional sources. The fractal basin boundary and other meth- ods are used to detect and quantify chaos in time-like geodesic motion of the particles, primarily by computing box-counting dimension of said basin boundary. Our results mainly consist of the dependence of the chaoticity of these systems on mass and radius of the additional source as well as conserved energy and angular momentum of the test particles. We compare our results to literature and expand on them.

Studium geodetického chaosu pomocí fraktálních metod

We study the dynamics of free test particles in a field of Schwarzschild black hole surrounded by an external exact thin axisymmetric solutions of Einstein's equations. Specifically, we use the Bach-Weyl ring and two member of the inverted Morgan-Morgan family of solutions as the additional sources. The fractal basin boundary and other meth- ods are used to detect and quantify chaos in time-like geodesic motion of the particles, primarily by computing box-counting dimension of said basin boundary. Our results mainly consist of the dependence of the chaoticity of these systems on mass and radius of the additional source as well as conserved energy and angular momentum of the test particles. We compare our results to literature and expand on them. 1Zkoumáme dynamiku volných testovacích částic v poli Schwarzschildovy černé díry obklopené statickým a axiálně symetrickým zdrojem popsaným přesným řešením Ein- steinových rovnic; konkrétně uvažujeme Bachův-Weylův prstenec a dva členy invertované třídy kontrarotujících disků Morgana & Morganové. K detekci a kvantifikaci chaosu v časupodobném geodetickém pohybu jsme použili metodu 'basin boundaries', spočívající v identifikaci a výpočtu dimenze hranic mezi množinami počátečních podmínek vedoucích k různým 'osudům' částic. Hlavním přínosem je popis závislosti chaotičnosti systému na hmotnosti a poloměru dodatečných zdrojů, a rovněž na energii a momentu hybnosti částic. Zjištění porovnáváme s výsledky získanými dříve jinými metodami. 1Ústav teoretické fyzikyInstitute of Theoretical PhysicsMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

Comparison of Brill waves with the fields of singular rings

Circular matter rings are a natural zero approximation of stationary and axially symmetric structures which appear in astrophysics. If the rings are infinitesimally thin (line sources), they are singular, which in the general relativistic description typically implies weird deformation of space in their vicinity. In particular, and contrary to the Newtonian picture, such rings even tend to behave in a strongly directional manner. One solution is to consider non-singular, extended sources (toroids), which may however be difficult to treat exactly and/or be unsatisfactory in other respects. In this thesis we check another option, namely to abandon the "real matter" completely and consider a non-singular source represented by mere curvature arranged, at least at some instant, in a pattern possessing the above symmetries. One such solution of Einstein's equations is known as the Brill waves; we study its properties at the moment of time symmetry (when it is momentarily static), in order to compare it with the space-times of matter rings.

Guanine bases in DNA G-quadruplex adopt nonplanar geometries owing to solvation and base pairing

The effect of base pairing and solvation on pyramidalization of the glycosidic nitrogen found in the residues of parallel G-quadruplex with NDB ID UDF062 is analyzed and explained with theoretical calculations. The extent of the pyramidalization depends on the local geometry of the 2′-deoxyguanosine residues, namely on their glycosidic torsion and sugar pucker, which are predetermined by the 3D-architecture of G-quadruplex. Pyramidal inversion of the glycosidic nitrogen found in 2′-deoxyguanosines of G-quadruplex is induced owing to site-specifically coordinated solvent. Different adiabatic structural constraints used for fixing the base-to-sugar orientation of 2′-deoxyguanosine in geometry optimizations result in different extents of pyramidalization and induce pyramidal inversion of the glycosidic nitrogen. These model geometry constraints helped us analyze the effect of real constraints represented by explicit molecular environment of selected residues of the G-quadruplex. The maximal extent of the glycosidic nitrogen pyramidalization found in the high-resolution crystal structure corresponds to the calculation to deformation energy of only 1 kcal mol–1. The out-of-plane deformations of nucleobases thus provide a way for compensating the site-specific external environmental stress on the G-quadruplex

Guanine bases in DNA G-quadruplex adopt nonplanar geometries owing to solvation and base pairing

The effect of base pairing and solvation on pyramidalization of the glycosidic nitrogen found in the residues of parallel G-quadruplex with NDB ID UDF062 is analyzed and explained with theoretical calculations. The extent of the pyramidalization depends on the local geometry of the 2′-deoxyguanosine residues, namely on their glycosidic torsion and sugar pucker, which are predetermined by the 3D-architecture of G-quadruplex. Pyramidal inversion of the glycosidic nitrogen found in 2′-deoxyguanosines of G-quadruplex is induced owing to site-specifically coordinated solvent. Different adiabatic structural constraints used for fixing the base-to-sugar orientation of 2′-deoxyguanosine in geometry optimizations result in different extents of pyramidalization and induce pyramidal inversion of the glycosidic nitrogen. These model geometry constraints helped us analyze the effect of real constraints represented by explicit molecular environment of selected residues of the G-quadruplex. The maximal extent of the glycosidic nitrogen pyramidalization found in the high-resolution crystal structure corresponds to the calculation to deformation energy of only 1 kcal mol–1. The out-of-plane deformations of nucleobases thus provide a way for compensating the site-specific external environmental stress on the G-quadruplex