Daniel Levy

Aarohi Srivastava, Abhinav Rastogi, Abhishek Rao et al. · allen-ai, amazon-science

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench currently consists of 204 tasks, contributed by 450 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting.

Chen Cheng, Daniel Levy, John C. Duchi

We study computational and statistical consequences of problem geometry in stochastic and online optimization. By focusing on constraint set and gradient geometry, we characterize the problem families for which stochastic- and adaptive-gradient methods are (minimax) optimal and, conversely, when nonlinear updates -- such as those mirror descent employs -- are necessary for optimal convergence. When the constraint set is quadratically convex, diagonally pre-conditioned stochastic gradient methods are minimax optimal. We provide quantitative converses showing that the ``distance'' of the underlying constraints from quadratic convexity determines the sub-optimality of subgradient methods. These results apply, for example, to any $\ell_p$-ball for $p < 2$, and the computation/accuracy tradeoffs they demonstrate exhibit a striking analogy to those in Gaussian sequence models.

Daniel Levy, Stefano Ermon

Policy optimization methods have shown great promise in solving complex reinforcement and imitation learning tasks. While model-free methods are broadly applicable, they often require many samples to optimize complex policies. Model-based methods greatly improve sample-efficiency but at the cost of poor generalization, requiring a carefully handcrafted model of the system dynamics for each task. Recently, hybrid methods have been successful in trading off applicability for improved sample-complexity. However, these have been limited to continuous action spaces. In this work, we present a new hybrid method based on an approximation of the dynamics as an expectation over the next state under the current policy. This relaxation allows us to derive a novel hybrid policy gradient estimator, combining score function and pathwise derivative estimators, that is applicable to discrete action spaces. We show significant gains in sample complexity, ranging between $1.7$ and $25\times$, when learning parameterized policies on Cart Pole, Acrobot, Mountain Car and Hand Mass. Our method is applicable to both discrete and continuous action spaces, when competing pathwise methods are limited to the latter.