We present a novel inductive generalization framework for RL from logical specifications. Many interesting tasks in RL environments have a natural inductive structure. These inductive tasks have similar overarching goals but they differ inductively in low-level predicates and distributions. We present a generalization procedure that leverages this inductive relationship to learn a higher-order function, a policy generator, that generates appropriately adapted policies for instances of an inductive task in a zero-shot manner. An evaluation of the proposed approach on a set of challenging control benchmarks demonstrates the promise of our framework in generalizing to unseen policies for long-horizon tasks.

Via an overparameterized linear model with Gaussian features, we provide conditions for good generalization for multiclass classification of minimum-norm interpolating solutions in an asymptotic setting where both the number of underlying features and the number of classes scale with the number of training points. The survival/contamination analysis framework for understanding the behavior of overparameterized learning problems is adapted to this setting, revealing that multiclass classification qualitatively behaves like binary classification in that, as long as there are not too many classes (made precise in the paper), it is possible to generalize well even in some settings where the corresponding regression tasks would not generalize. Besides various technical challenges, it turns out that the key difference from the binary classification setting is that there are relatively fewer positive training examples of each class in the multiclass setting as the number of classes increases, making the multiclass problem "harder" than the binary one.

Paradigmatic problems in supervised machine learning (ML) involve predicting an output response from an input, based on patterns extracted from a (training) dataset. In classification, the output response is (finitely) discrete and we need to classify input data into one of these discrete categories. In regression, the output is continuous, typically a real number or a vector. Owing to this important distinction in output response, the two tasks are typically treated differently. The differences in treatment manifest in two phases of modern ML: optimization (training), which consists of an algorithmic procedure to extract a predictor from the training data, typically by minimizing the training loss (also called empirical risk); and generalization (testing), which consists of an evaluation of the obtained predictor on a separate test, or validation, dataset. Traditionally, the choice of loss functions for both phases is starkly different across classification and regression tasks. The squared-loss function is typically used both for the training and the testing phases in regression. In contrast, the hinge or logistic (cross-entropy for multi-class problems) loss functions are typically used in the training phase of classification, while the very different 0-1 loss function is used for testing.