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The growing capabilities and increasingly widespread deployment of AI systems necessitate robust benchmarks for measuring their cooperative capabilities. Unfortunately, most multi-agent benchmarks are either zero-sum or purely cooperative, providing limited opportunities for such measurements. We introduce a general-sum variant of the zero-sum board game Diplomacy -- called Welfare Diplomacy -- in which players must balance investing in military conquest and domestic welfare. We argue that Welfare Diplomacy facilitates both a clearer assessment of and stronger training incentives for cooperative capabilities. Our contributions are: (1) proposing the Welfare Diplomacy rules and implementing them via an open-source Diplomacy engine; (2) constructing baseline agents using zero-shot prompted language models; and (3) conducting experiments where we find that baselines using state-of-the-art models attain high social welfare but are exploitable. Our work aims to promote societal safety by aiding researchers in developing and assessing multi-agent AI systems. Code to evaluate Welfare Diplomacy and reproduce our experiments is available at https://github.com/mukobi/welfare-diplomacy.

To optimally coordinate with others in cooperative games, it is often crucial to have information about one's collaborators: successful driving requires understanding which side of the road to drive on. However, not every feature of collaborators is strategically relevant: the fine-grained acceleration of drivers may be ignored while maintaining optimal coordination. We show that there is a well-defined dichotomy between strategically relevant and irrelevant information. Moreover, we show that, in dynamic games, this dichotomy has a compact representation that can be efficiently computed via a Bellman backup operator. We apply this algorithm to analyze the strategically relevant information for tasks in both a standard and a partially observable version of the Overcooked environment. Theoretical and empirical results show that our algorithms are significantly more efficient than baselines. Videos are available at https://minknowledge.github.io., Comment: To be published at ICML 2023

The District of Columbia Public Schools (DCPS) has prioritized efforts to support students' social and emotional learning (SEL) competencies, such as perseverance and social awareness. To measure students' SEL competencies and the school experiences that promote SEL competencies (school climate), DCPS began administering annual surveys to students, teachers, and parents in 2017/18. DCPS partnered with the Mid-Atlantic Regional Educational Laboratory to study how the district could use these surveys to improve students' outcomes. The study found the following: (1) Students' SEL competencies and school experiences are the most favorable in elementary school and the least favorable in middle school and the beginning of high school. This pattern suggests that schools might provide targeted supports before or during grades 6-10 to promote SEL competencies and school experiences when students need the most support; (2) The trajectories of students' SEL competencies and school experiences differed in different schools, to a similar degree as trajectories in academic measures like test scores. To understand why changes in SEL competencies and school experiences differ across schools, DCPS could explore differences in practices between schools with better and worse trajectories. In addition, DCPS could provide targeted support to schools with lower levels of positive change; (3) Of the SEL competencies and school experiences in DCPS's survey, self-management--how well students control their emotions, thoughts, and behavior--is most related to students' later academic outcomes. Programs or interventions that target self-management might have the most potential for improving students' outcomes compared to those that target other SEL competencies or school experiences; (4) In statistical models designed to predict students' future academic outcomes, SEL competency and school experience data add little accuracy beyond prior academic outcomes (such as achievement test scores and attendance) and demographic characteristics. Prior academic outcomes and demographic characteristics predict later outcomes with a high degree of accuracy, and they may implicitly incorporate the SEL competencies and school experiences. These findings suggest that DCPS would not need to use SEL competencies and school experiences to identify whether or not students are at risk of poor academic outcomes; and (5) Student, teacher, and parent reports on SEL competencies and school experiences are positively related across schools, but they also exhibit systematic differences, suggesting that some respondent groups may not be aligned in their view of SEL competencies and school experiences. These differences may serve as a tool to help DCPS target efforts to improve communication among students, teachers, and parents.

We present the photometric data from TESS for two known ZZ Ceti stars, PG 1541+651 and BPM 31594. Before TESS, both objects only had observations from short runs from ground-based facilities, with three and one period detected, respectively. The TESS data allowed the detection of multiple periodicities, 12 for PG 1541$+$651, and six for BPM 31594, which enables us to perform a detailed asteroseismological study. For both objects we found a representative asteroseismic model with canonical stellar mass ~ 0.61 Msun and thick hydrogen envelopes, thicker than 10^(-5.3) M_*. The detection of triplets in the Fourier transform also allowed us to estimate mean rotation periods, being ~22 h for PG 1541+651 and 11.6 h for BPM 31594, which is consistent with range of values reported for other ZZ Ceti stars., Comment: 12 pages, 11 figures. Accepted for publication in MNRAS

The identification of a deterministic finite automaton (DFA) from labeled examples is a well-studied problem in the literature; however, prior work focuses on the identification of monolithic DFAs. Although monolithic DFAs provide accurate descriptions of systems' behavior, they lack simplicity and interpretability; moreover, they fail to capture sub-tasks realized by the system and introduce inductive biases away from the inherent decomposition of the overall task. In this paper, we present an algorithm for learning conjunctions of DFAs from labeled examples. Our approach extends an existing SAT-based method to systematically enumerate Pareto-optimal candidate solutions. We highlight the utility of our approach by integrating it with a state-of-the-art algorithm for learning DFAs from demonstrations. Our experiments show that the algorithm learns sub-tasks realized by the labeled examples, and it is scalable in the domains of interest., Comment: Preprint, under review

In a Stackelberg game, a leader commits to a randomized strategy, and a follower chooses their best strategy in response. We consider an extension of a standard Stackelberg game, called a discrete-time dynamic Stackelberg game, that has an underlying state space that affects the leader's rewards and available strategies and evolves in a Markovian manner depending on both the leader and follower's selected strategies. Although standard Stackelberg games have been utilized to improve scheduling in security domains, their deployment is often limited by requiring complete information of the follower's utility function. In contrast, we consider scenarios where the follower's utility function is unknown to the leader; however, it can be linearly parameterized. Our objective then is to provide an algorithm that prescribes a randomized strategy to the leader at each step of the game based on observations of how the follower responded in previous steps. We design a no-regret learning algorithm that, with high probability, achieves a regret bound (when compared to the best policy in hindsight) which is sublinear in the number of time steps; the degree of sublinearity depends on the number of features representing the follower's utility function. The regret of the proposed learning algorithm is independent of the size of the state space and polynomial in the rest of the parameters of the game. We show that the proposed learning algorithm outperforms existing model-free reinforcement learning approaches., Comment: Preprint, under review

Pulsating low-mass white dwarf stars are white dwarfs with stellar masses between 0.30~M$_{\odot}$ and 0.45~M$_{\odot}$ that show photometric variability due to gravity-mode pulsations. Within this mass range, they can harbour both a helium- and hybrid-core, depending if the progenitor experienced helium-core burning during the pre-white dwarf evolution. SDSS J115219.99$+$024814.4 is an eclipsing binary system where both components are low-mass white dwarfs, with stellar masses of 0.362$\pm$0.014~M$_{\odot}$ and 0.325$\pm$0.013~M$_{\odot}$. In particular, the less massive component is a pulsating star, showing at least three pulsation periods of $\sim$1314 s, $\sim$1069 s and $\sim$582.9 s. This opens the way to use asteroseismology as a tool to uncover its inner chemical structure, in combination with the information obtained using the light-curve modelling of the eclipses. To this end, using binary evolutionary models leading to helium- and hybrid-core white dwarfs, we compute adiabatic pulsations for $\ell=1$ and $\ell=2$ gravity modes with \texttt{Gyre}. We found that the pulsating component of the SDSS J115219.99$+$024814.4 system must have a hydrogen envelope thinner that the value obtained from binary evolution computations, independently of the inner composition. Finally, from our asteroseismological study, we find a best fit model characterised by T$_{\rm e ff}=10\, 917$ K, M=0.338~M$_{\odot}$, M$_{\rm H}=10^{-6}$~M$_{\odot}$ with the inner composition of a hybrid WD., Comment: 10 pages, 9 figures. Accepted for publication by MNRAS

In this work, we study the problem of actively classifying the attributes of dynamical systems characterized as a finite set of Markov decision process (MDP) models. We are interested in finding strategies that actively interact with the dynamical system and observe its reactions so that the attribute of interest is classified efficiently with high confidence. We present a decision-theoretic framework based on partially observable Markov decision processes (POMDPs). The proposed framework relies on assigning a classification belief (a probability distribution) to the attributes of interest. Given an initial belief, a confidence level over which a classification decision can be made, a cost bound, safe belief sets, and a finite time horizon, we compute POMDP strategies leading to classification decisions. We present three different algorithms to compute such strategies. The first algorithm computes the optimal strategy exactly by value iteration. To overcome the computational complexity of computing the exact solutions, we propose a second algorithm based on adaptive sampling and a third based on a Monte Carlo tree search to approximate the optimal probability of reaching a classification decision. We illustrate the proposed methodology using examples from medical diagnosis, security surveillance, and wildlife classification., Comment: arXiv admin note: substantial text overlap with arXiv:1810.00097

We perform ground based photometric observations of 22 DA white dwarf stars, 10 already known ZZ Cetis and 12 candidates with atmospheric parameters inside the classical instability strip. We report on the discovery of four new variable DA white dwarf stars. Two objects are near the middle of the instability strip, SDSS J082804.63+094956.6 and SDSS J094929.09+101918.8, and two red edge pulsators, GD 195 and L495-82. In addition, we classified four objects as possible variables, since evidence of variability was detected in the light curve, but the S/N was not sufficient to establish a definite detection. Follow-up observations were performed for 10 know ZZ Ceti stars to verify period stability and search for new periodicities. For each confirmed variable, we perform a detailed asteroseismological fit and compare the structural parameters obtained from the best fit models with those obtained from spectroscopy and photometry from Gaia. Finally we present a study of the asteroseismological properties of a sample of 91 ZZ Ceti stars., Comment: 18 pages, 12 figures. Accepted for publication in MNRAS

One approach for feedback control using high dimensional and rich sensor measurements is to classify the measurement into one out of a finite set of situations, each situation corresponding to a (known) control action. This approach computes a control action without estimating the state. Such classifiers are typically learned from a finite amount of data using supervised machine learning algorithms. We model the closed-loop system resulting from control with feedback from classifier outputs as a piece-wise affine differential inclusion. We show how to train a linear classifier based on performance measures related to learning from data and the local stability properties of the resulting closed-loop system. The training method is based on the projected gradient descent algorithm. We demonstrate the advantage of training classifiers using control-theoretic properties on a case study involving navigation using range-based sensors., Comment: 9 pages, conference

We present a study of the dependence of the mass-radius relation for DA white dwarf stars on the hydrogen envelope mass and the impact on the value of log g, and thus the determination of the stellar mass. We employ a set of full evolutionary carbon-oxygen core white dwarf sequences with white dwarf mass between 0.493 and 1.05 Msun. Computations of the pre-white dwarf evolution uncovers an intrinsic dependence of the maximum mass of the hydrogen envelope with stellar mass, i.e., it decreases when the total mass increases. We find that a reduction of the hydrogen envelope mass can lead to a reduction in the radius of the model of up to ~12%. This translates directly into an increase in log g for a fixed stellar mass, that can reach up to 0.11 dex, mainly overestimating the determinations of stellar mass from atmospheric parameters. Finally, we find a good agreement between the results from the theoretical mass-radius relation and observations from white dwarfs in binary systems. In particular, we find a thin hydrogen mass of MH ~ 2 10^-8 Msun, for 40 Eridani B, in agreement with previous determinations. For Sirius B, the spectroscopic mass is 4.3% lower than the dynamical mass. However, the values of mass and radius from gravitational redshift observations are compatible with the theoretical mass-radius relation for a thick hydrogen envelope of MH = 2 10^-6 Msun., Comment: Accepted for publication in MNRAS

We explore the evolution of hydrogen-rich and hydrogen-deficient white dwarf stars with masses between 1.012 and 1.307 Msun, and initial metallicity of Z=0.02. These sequences are the result of main sequence stars with masses between 8.8 and 11.8 Msun. The simulations were performed with MESA, starting at the zero-age main sequence, through thermally pulsing and mass-loss phases, ending at the white dwarfs cooling sequence. We present reliable chemical profiles for the whole mass range considered, covering the different expected central compositions, i.e. C/O, O/Ne and Ne/O/Mg, and its dependence with the stellar mass. In addition, we present detailed chemical profiles of hybrid C/O-O/Ne core white dwarfs, found in the mass range between 1.024 and 1.15 Msun. We present the initial-to-final mass relation, mass-radius relation, and cooling times considering the effects of atmosphere and core composition., Comment: 17 pages, 16 figures, 3 tables, accepted for publication in MNRAS. Cooling tracks available at ftp://cdsarc.u-strasbg.fr/pub/cats/J/MNRAS/480/1547

We introduce a novel architecture and computational framework for formal, automated analysis of systems with a broad set of nonlinearities in the feedback loop, such as neural networks, vision controllers, switched systems, and even simple programs. We call this computational structure an affine multiplexing network (AMN). The architecture is based on interconnections of two basic conceptual building blocks: multiplexers ($\mu$), and affine transformations ($\alpha$). When attached together appropriately, these building blocks translate to conjunctions and disjunctions of affine statements, resulting in an encoding of the network into satisfiability modulo theory (SMT), mixed integer programming, and sequential convex optimization solvers. We show how to formulate and verify system properties like stability and robustness, how to compute margins, and how to verify performance through a sequence of SMT queries. As illustration, we use the framework to verify closed loop, possibly nonlinear dynamical systems that contain neural networks in the loop, and hint at a number of extensions that can make AMNs a potent playground for interfacing between machine learning, control, convex and nonconvex optimization, and formal methods., Comment: 30 pages, 12 figures