Previous theoretical results pertaining to meta-learning on sequences build on contrived and convoluted mixing time assumptions. We introduce new information-theoretic tools that lead to a concise yet general decomposition of error for a Bayes optimal predictor into two components: meta-learning error and intra-task error. These tools unify analyses across many meta-learning challenges. To illustrate, we apply them to establish new results about in-context learning with transformers and corroborate existing results a simple linear setting. Our theoretical results characterize how error decays in both the number of training sequences and sequence lengths. Our results are very general; for example, they avoid contrived mixing time assumptions made by all prior results that establish decay of error with sequence length.

Each year, deep learning demonstrate new and improved empirical results with deeper and wider neural networks. Meanwhile, with existing theoretical frameworks, it is difficult to analyze networks deeper than two layers without resorting to counting parameters or encountering sample complexity bounds that are exponential in depth. Perhaps it may be fruitful to try to analyze modern machine learning under a different lens. In this paper, we propose a novel information-theoretic framework with its own notions of regret and sample complexity for analyzing the data requirements of machine learning. We use this framework to study the sample complexity of learning from data generated by deep ReLU neural networks and deep networks that are infinitely wide but have a bounded sum of weights. We establish that the sample complexity of learning under these data generating processes is at most linear and quadratic, respectively, in network depth.

It is often difficult to hand-specify what the correct reward function is for a task, so researchers have instead aimed to learn reward functions from human behavior or feedback. The types of behavior interpreted as evidence of the reward function have expanded greatly in recent years. We've gone from demonstrations, to comparisons, to reading into the information leaked when the human is pushing the robot away or turning it off. And surely, there is more to come. How will a robot make sense of all these diverse types of behavior? Our key observation is that different types of behavior can be interpreted in a single unifying formalism - as a reward-rational choice that the human is making, often implicitly. We use this formalism to survey prior work through a unifying lens, and discuss its potential use as a recipe for interpreting new sources of information that are yet to be uncovered.

When robot manipulators decide how to reach for an object, hand it over, or obey some task constraint, they implicitly assume a Euclidean distance metric in their configuration space. Their notion of what makes a configuration closer or further is dictated by this assumption. But different distance metrics will lead to different solutions. What is efficient under a Euclidean metric might not necessarily look the most efficient or natural to a person observing the robot. In this paper, we analyze the effect of the metric on robot behavior, examining both Euclidean, as well as non-Euclidean metrics - metrics that make certain joints cheaper, or that correlate different joints. Our user data suggests that tasks on a 3DOF arm and the Jaco 7DOF arm can typically be grouped into ones where a Euclidean metric works well, and tasks where that is no longer the case: there, surprisingly, penalizing elbow motion (and sometimes correlating the shoulder and wrist) leads to solutions that are more aligned with what users prefer.