We consider a number of questions related to tradeoffs between reward and regret in repeated gameplay between two agents. To facilitate this, we introduce a notion of $\textit{generalized equilibrium}$ which allows for asymmetric regret constraints, and yields polytopes of feasible values for each agent and pair of regret constraints, where we show that any such equilibrium is reachable by a pair of algorithms which maintain their regret guarantees against arbitrary opponents. As a central example, we highlight the case one agent is no-swap and the other's regret is unconstrained. We show that this captures an extension of $\textit{Stackelberg}$ equilibria with a matching optimal value, and that there exists a wide class of games where a player can significantly increase their utility by deviating from a no-swap-regret algorithm against a no-swap learner (in fact, almost any game without pure Nash equilibria is of this form). Additionally, we make use of generalized equilibria to consider tradeoffs in terms of the opponent's algorithm choice. We give a tight characterization for the maximal reward obtainable against $\textit{some}$ no-regret learner, yet we also show a class of games in which this is bounded away from the value obtainable against the class of common "mean-based" no-regret algorithms. Finally, we consider the question of learning reward-optimal strategies via repeated play with a no-regret agent when the game is initially unknown. Again we show tradeoffs depending on the opponent's learning algorithm: the Stackelberg strategy is learnable in exponential time with any no-regret agent (and in polynomial time with any no-$\textit{adaptive}$-regret agent) for any game where it is learnable via queries, and there are games where it is learnable in polynomial time against any no-swap-regret agent but requires exponential time against a mean-based no-regret agent.

For domains in which a recommender provides repeated content suggestions, agent preferences may evolve over time as a function of prior recommendations, and algorithms must take this into account for long-run optimization. Recently, Agarwal and Brown (2022) introduced a model for studying recommendations when agents' preferences are adaptive, and gave a series of results for the case when agent preferences depend {\it uniformly} on their history of past selections. Here, the recommender shows a $k$-item menu (out of $n$) to the agent at each round, who selects one of the $k$ items via their history-dependent {\it preference model}, yielding a per-item adversarial reward for the recommender. We expand this setting to {\it non-uniform} preferences, and give a series of results for {\it $\gamma$-discounted} histories. For this problem, the feasible regret benchmarks can depend drastically on varying conditions. In the ``large $\gamma$'' regime, we show that the previously considered benchmark, the ``EIRD set'', is attainable for any {\it smooth} model, relaxing the ``local learnability'' requirement from the uniform memory case. We introduce ``pseudo-increasing'' preference models, for which we give an algorithm which can compete against any item distribution with small uniform noise (the ``smoothed simplex''). We show NP-hardness results for larger regret benchmarks in each case. We give another algorithm for pseudo-increasing models (under a restriction on the adversarial nature of the reward functions), which works for any $\gamma$ and is faster when $\gamma$ is sufficiently small, and we show a super-polynomial regret lower bound with respect to EIRD for general models in the ``small $\gamma$'' regime. We conclude with a pair of algorithms for the memoryless case.

Machine learning methods have seen increased application to geospatial environmental problems, such as precipitation nowcasting, haze forecasting, and crop yield prediction. However, many of the machine learning methods applied to mosquito population and disease forecasting do not inherently take into account the underlying spatial structure of the given data. In our work, we apply a spatially aware graph neural network model consisting of GraphSAGE layers to forecast the presence of West Nile virus in Illinois, to aid mosquito surveillance and abatement efforts within the state. More generally, we show that graph neural networks applied to irregularly sampled geospatial data can exceed the performance of a range of baseline methods including logistic regression, XGBoost, and fully-connected neural networks.

We provide a differentially private algorithm for producing synthetic data simultaneously useful for multiple tasks: marginal queries and multitask machine learning (ML). A key innovation in our algorithm is the ability to directly handle numerical features, in contrast to a number of related prior approaches which require numerical features to be first converted into {high cardinality} categorical features via {a binning strategy}. Higher binning granularity is required for better accuracy, but this negatively impacts scalability. Eliminating the need for binning allows us to produce synthetic data preserving large numbers of statistical queries such as marginals on numerical features, and class conditional linear threshold queries. Preserving the latter means that the fraction of points of each class label above a particular half-space is roughly the same in both the real and synthetic data. This is the property that is needed to train a linear classifier in a multitask setting. Our algorithm also allows us to produce high quality synthetic data for mixed marginal queries, that combine both categorical and numerical features. Our method consistently runs 2-5x faster than the best comparable techniques, and provides significant accuracy improvements in both marginal queries and linear prediction tasks for mixed-type datasets.

In this paper, computer-based techniques for stylistic analysis of paintings are applied to the five panels of the 14th century Peruzzi Altarpiece by Giotto di Bondone. Features are extracted by combining a dual-tree complex wavelet transform with a hidden Markov tree (HMT) model. Hierarchical clustering is used to identify stylistic keywords in image patches, and keyword frequencies are calculated for sub-images that each contains many patches. A generative hierarchical Bayesian model learns stylistic patterns of keywords; these patterns are then used to characterize the styles of the sub-images; this in turn, permits to discriminate between paintings. Results suggest that such unsupervised probabilistic topic models can be useful to distill characteristic elements of style.