Adaptive Crowdsourcing Via Self-Supervised Learning

Common crowdsourcing systems average estimates of a latent quantity of interest provided by many crowdworkers to produce a group estimate. We develop a new approach -- predict-each-worker -- that leverages self-supervised learning and a novel aggregation scheme. This approach adapts weights assigned to crowdworkers based on estimates they provided for previous quantities. When skills vary across crowdworkers or their estimates correlate, the weighted sum offers a more accurate group estimate than the average. Existing algorithms such as expectation maximization can, at least in principle, produce similarly accurate group estimates. However, their computational requirements become onerous when complex models, such as neural networks, are required to express relationships among crowdworkers. Predict-each-worker accommodates such complexity as well as many other practical challenges. We analyze the efficacy of predict-each-worker through theoretical and computational studies. Among other things, we establish asymptotic optimality as the number of engagements per crowdworker grows.

An Information-Theoretic Analysis of In-Context Learning

Previous theoretical results pertaining to meta-learning on sequences build on contrived assumptions and are somewhat convoluted. We introduce new information-theoretic tools that lead to an elegant and very general decomposition of error into three components: irreducible error, 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. Our theoretical results characterizes 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.

Continual Learning as Computationally Constrained Reinforcement Learning

An agent that efficiently accumulates knowledge to develop increasingly sophisticated skills over a long lifetime could advance the frontier of artificial intelligence capabilities. The design of such agents, which remains a long-standing challenge of artificial intelligence, is addressed by the subject of continual learning. This monograph clarifies and formalizes concepts of continual learning, introducing a framework and set of tools to stimulate further research.

An Information-Theoretic Analysis of Compute-Optimal Neural Scaling Laws

We study the compute-optimal trade-off between model and training data set sizes for large neural networks. Our result suggests a linear relation similar to that supported by the empirical analysis of Chinchilla. While that work studies transformer-based large language models trained on the MassiveText corpus (gopher), as a starting point for development of a mathematical theory, we focus on a simpler learning model and data generating process, each based on a neural network with a sigmoidal output unit and single hidden layer of ReLU activation units. We establish an upper bound on the minimal information-theoretically achievable expected error as a function of model and data set sizes. We then derive allocations of computation that minimize this bound. We present empirical results which suggest that this approximation correctly identifies an asymptotic linear compute-optimal scaling. This approximation can also generate new insights. Among other things, it suggests that, as the input space dimension or latent space complexity grows, as might be the case for example if a longer history of tokens is taken as input to a language model, a larger fraction of the compute budget should be allocated to growing the learning model rather than training data set.

Is Stochastic Gradient Descent Near Optimal?

The success of neural networks over the past decade has established them as effective models for many relevant data generating processes. Statistical theory on neural networks indicates graceful scaling of sample complexity. For example, Joen & Van Roy (arXiv:2203.00246) demonstrate that, when data is generated by a ReLU teacher network with $W$ parameters, an optimal learner needs only $\tilde{O}(W/\epsilon)$ samples to attain expected error $\epsilon$. However, existing computational theory suggests that, even for single-hidden-layer teacher networks, to attain small error for all such teacher networks, the computation required to achieve this sample complexity is intractable. In this work, we fit single-hidden-layer neural networks to data generated by single-hidden-layer ReLU teacher networks with parameters drawn from a natural distribution. We demonstrate that stochastic gradient descent (SGD) with automated width selection attains small expected error with a number of samples and total number of queries both nearly linear in the input dimension and width. This suggests that SGD nearly achieves the information-theoretic sample complexity bounds of Joen & Van Roy (arXiv:2203.00246) in a computationally efficient manner. An important difference between our positive empirical results and the negative theoretical results is that the latter address worst-case error of deterministic algorithms, while our analysis centers on expected error of a stochastic algorithm.

Sample Complexity versus Depth: An Information Theoretic Analysis

Deep learning has proven effective across a range of data sets. In light of this, a natural inquiry is: "for what data generating processes can deep learning succeed?" In this work, we study the sample complexity of learning multilayer data generating processes of a sort for which deep neural networks seem to be suited. We develop general and elegant information-theoretic tools that accommodate analysis of any data generating process -- shallow or deep, parametric or nonparametric, noiseless or noisy. We then use these tools to characterize the dependence of sample complexity on the depth of multilayer processes. Our results indicate roughly linear dependence on depth. This is in contrast to previous results that suggest exponential or high-order polynomial dependence.

Learning Latent Actions to Control Assistive Robots

Assistive robot arms enable people with disabilities to conduct everyday tasks on their own. These arms are dexterous and high-dimensional; however, the interfaces people must use to control their robots are low-dimensional. Consider teleoperating a 7-DoF robot arm with a 2-DoF joystick. The robot is helping you eat dinner, and currently you want to cut a piece of tofu. Today's robots assume a pre-defined mapping between joystick inputs and robot actions: in one mode the joystick controls the robot's motion in the x-y plane, in another mode the joystick controls the robot's z-yaw motion, and so on. But this mapping misses out on the task you are trying to perform! Ideally, one joystick axis should control how the robot stabs the tofu and the other axis should control different cutting motions. Our insight is that we can achieve intuitive, user-friendly control of assistive robots by embedding the robot's high-dimensional actions into low-dimensional and human-controllable latent actions. We divide this process into three parts. First, we explore models for learning latent actions from offline task demonstrations, and formalize the properties that latent actions should satisfy. Next, we combine learned latent actions with autonomous robot assistance to help the user reach and maintain their high-level goals. Finally, we learn a personalized alignment model between joystick inputs and latent actions. We evaluate our resulting approach in four user studies where non-disabled participants reach marshmallows, cook apple pie, cut tofu, and assemble dessert. We then test our approach with two disabled adults who leverage assistive devices on a daily basis.