We give an efficient algorithm for producing multi-dimensional forecasts in an online adversarial environment that have low bias subject to any polynomial number of conditioning events, that can depend both on external context and on our predictions themselves. We demonstrate the use of this algorithm with several applications. We show how to make predictions that can be transparently consumed by any polynomial number of downstream decision makers with different utility functions, guaranteeing them diminishing swap regret at optimal rates. We also give the first efficient algorithms for guaranteeing diminishing conditional regret in online combinatorial optimization problems for an arbitrary polynomial number of conditioning events --- i.e. on an arbitrary number of intersecting subsequences determined both by context and our own predictions. Finally, we give the first efficient algorithm for online multicalibration with $O(T^{2/3})$ rates in the ECE metric.

Existing algorithms for online conformal prediction—guaranteeing marginal coverage in adversarial settings—are variants of online gradient descent (OGD), but their analyses of worst-case coverage do not follow from the regret guarantee of OGD. What is the relationship between no-regret learning and online conformal prediction? We observe that although standard regret guarantees imply marginal coverage in i.i.d. settings, this connection fails as soon as we either move to adversarial environments or ask for group conditional coverage. On the other hand, we show a tight connection between threshold calibrated coverage and swap-regret in adversarial settings, which extends to group-conditional (multi-valid) coverage. We also show that algorithms in the follow the regularized leader family of no regret learning algorithms (which includes online gradient descent) can be used to give group-conditional coverage guarantees in adversarial settings for arbitrary grouping functions. Via this connection we analyze and conduct experiments using a multi-group generalization of the ACI algorithm of Gibbs & Candes (2021).

The goal of active learning for program synthesis is to synthesize the desired program by asking targeted questions that minimize user interaction. While prior work has explored active learning in the purely symbolic setting, such techniques are inadequate for the increasingly popular paradigm of neurosymbolic program synthesis , where the synthesized program incorporates neural components. When applied to the neurosymbolic setting, such techniques can —and, in practice, do — return an unintended program due to mispredictions of neural components. This paper proposes a new active learning technique that can handle the unique challenges posed by neural network mispredictions. Our approach is based upon a new evaluation strategy called constrained conformal evaluation (CCE) , which accounts for neural mispredictions while taking into account user-provided feedback. Our proposed method iteratively makes CCE more precise until all remaining programs are guaranteed to be observationally equivalent. We have implemented this method in a tool called SmartLabel and experimentally evaluated it on three neurosymbolic domains. Our results demonstrate that SmartLabel identifies the ground truth program for 98% of the benchmarks, requiring under 5 rounds of user interaction on average. In contrast, prior techniques for active learning are only able to converge to the ground truth program for at most 65% of the benchmarks.

We derive generalization bounds on learning algorithms through algorithm capacity and a vector representation of inductive bias. Leveraging the algorithmic search framework, a formalism for casting machine learning as a type of search, we present a unified interpretation of the upper bounds of generalization error in terms of a vector representation of bias and the mutual information between the hypothesis and the dataset.

We give a simple, generic conformal prediction method for sequential prediction that achieves target empirical coverage guarantees on adversarial data. It is computationally lightweight --- comparable to split conformal prediction --- but does not require having a held-out validation set, and so all data can be used for training models from which to derive a conformal score. Furthermore, it gives stronger than marginal coverage guarantees in two ways. First, it gives threshold-calibrated prediction sets that have correct empirical coverage even conditional on the threshold used to form the prediction set from the conformal score. Second, the user can specify an arbitrary collection of subsets of the feature space --- possibly intersecting --- and the coverage guarantees will also hold conditional on membership in each of these subsets. We call our algorithm MVP, short for MultiValid Prediction. We give both theory and an extensive set of empirical evaluations.

UV radiation has been used as a disinfection strategy to deactivate a wide range of pathogens, but existing irradiation strategies do not ensure sufficient exposure of all environmental surfaces and/or require long disinfection times. We present a near-optimal coverage planner for mobile UV disinfection robots. The formulation optimizes the irradiation time efficiency, while ensuring that a sufficient dosage of radiation is received by each surface. The trajectory and dosage plan are optimized taking collision and light occlusion constraints into account. We propose a two-stage scheme to approximate the solution of the induced NP-hard optimization, and, for efficiency, perform key irradiance and occlusion calculations on a GPU. Empirical results show that our technique achieves more coverage for the same exposure time as strategies for existing UV robots, can be used to compare UV robot designs, and produces near-optimal plans.

Maximum parsimony reconciliation is a fundamental technique for studying the evolutionary histories of pairs of entities such as genes and species, parasites and hosts, and species and their biogeographical habitats. In these contexts, reconciliation is generally performed using the duplication-transfer-loss (DTL) model in a maximum parsimony framework. While efficient maximum parsimony reconciliation algorithms are known for the DTL model, the number of such reconciliations can grow exponentially with the sizes of the two phylogenetic trees. Choosing a maximum parsimony reconciliation arbitrarily may lead to conclusions that are not supported, and may even be contradicted, by other equally optimal reconciliations. This paper addresses the fundamental problem of how well a single reconciliation can represent the entire space of optimal reconciliations.