This paper proposes a new method for differentiating through optimal trajectories arising from non-convex, constrained discrete-time optimal control (COC) problems using the implicit function theorem (IFT). Previous works solve a differential Karush-Kuhn-Tucker (KKT) system for the trajectory derivative, and achieve this efficiently by solving an auxiliary Linear Quadratic Regulator (LQR) problem. In contrast, we directly evaluate the matrix equations which arise from applying variable elimination on the Lagrange multiplier terms in the (differential) KKT system. By appropriately accounting for the structure of the terms within the resulting equations, we show that the trajectory derivatives scale linearly with the number of timesteps. Furthermore, our approach allows for easy parallelization, significantly improved scalability with model size, direct computation of vector-Jacobian products and improved numerical stability compared to prior works. As an additional contribution, we unify prior works, addressing claims that computing trajectory derivatives using IFT scales quadratically with the number of timesteps. We evaluate our method on a both synthetic benchmark and four challenging, learning from demonstration benchmarks including a 6-DoF maneuvering quadrotor and 6-DoF rocket powered landing.

The Stable Diffusion model is a prominent text-to-image generation model that relies on a text prompt as its input, which is encoded using the Contrastive Language-Image Pre-Training (CLIP). However, text prompts have limitations when it comes to incorporating implicit information from reference images. Existing methods have attempted to address this limitation by employing expensive training procedures involving millions of training samples for image-to-image generation. In contrast, this paper demonstrates that the CLIP model, as utilized in Stable Diffusion, inherently possesses the ability to instantaneously convert images into text prompts. Such an image-to-prompt conversion can be achieved by utilizing a linear projection matrix that is calculated in a closed form. Moreover, the paper showcases that this capability can be further enhanced by either utilizing a small amount of similar-domain training data (approximately 100 images) or incorporating several online training steps (around 30 iterations) on the reference images. By leveraging these approaches, the proposed method offers a simple and flexible solution to bridge the gap between images and text prompts. This methodology can be applied to various tasks such as image variation and image editing, facilitating more effective and seamless interaction between images and textual prompts.

Minimising upper bounds on the population risk or the generalisation gap has been widely used in structural risk minimisation (SRM) -- this is in particular at the core of PAC-Bayesian learning. Despite its successes and unfailing surge of interest in recent years, a limitation of the PAC-Bayesian framework is that most bounds involve a Kullback-Leibler (KL) divergence term (or its variations), which might exhibit erratic behavior and fail to capture the underlying geometric structure of the learning problem -- hence restricting its use in practical applications.As a remedy, recent studies have attempted to replace the KL divergence in the PAC-Bayesian bounds with the Wasserstein distance. Even though these bounds alleviated the aforementioned issues to a certain extent, they either hold in expectation, are for bounded losses, or are nontrivial to minimize in an SRM framework. In this work, we contribute to this line of research and prove novel Wasserstein distance-based PAC-Bayesian generalisation bounds for both batch learning with independent and identically distributed (i.i.d.) data, and online learning with potentially non-i.i.d.

In many applications, learning systems are required to process continuous non-stationary data streams.We study this problem in an online learning framework and propose an algorithm that can deal with adversarial time-varying and nonlinear constraints.As we show in our work, the algorithm called Constraint Violation Velocity Projection (CVV-Pro) achieves $\sqrt{T}$ regret and converges to the feasible set at a rate of $1/\sqrt{T}$, despite the fact that the feasible set is slowly time-varying and a priori unknown to the learner. CVV-Pro only relies on local sparse linear approximations of the feasible set and therefore avoids optimizing over the entire set at each iteration, which is in sharp contrast to projected gradients or Frank-Wolfe methods. We also empirically evaluate our algorithm on two-player games, where the players are subjected to a shared constraint.

In a standard view of the reinforcement learning problem, an agent's goal is to efficiently identify a policy that maximizes long-term reward. However, this perspective is based on a restricted view of learning as finding a solution, rather than treating learning as endless adaptation. In contrast, continual reinforcement learning refers to the setting in which the best agents never stop learning. Despite the importance of continual reinforcement learning, the community lacks a simple definition of the problem that highlights its commitments and makes its primary concepts precise and clear. To this end, this paper is dedicated to carefully defining the continual reinforcement learning problem. We formalize the notion of agents that "never stop learning" through a new mathematical language for analyzing and cataloging agents. Using this new language, we define a continual learning agent as one that can be understood as carrying out an implicit search process indefinitely, and continual reinforcement learning as the setting in which the best agents are all continual learning agents. We provide two motivating examples, illustrating that traditional views of multi-task reinforcement learning and continual supervised learning are special cases of our definition.

Neural MMO 2.0 is a massively multi-agent and multi-task environment for reinforcement learning research. This version features a novel task-system that broadens the range of training settings and poses a new challenge in generalization: evaluation on and against tasks, maps, and opponents never seen during training. Maps are procedurally generated with 128 agents in the standard setting and 1-1024 supported overall. Version 2.0 is a complete rewrite of its predecessor with three-fold improved performance, effectively addressing simulation bottlenecks in online training. Enhancements to compatibility enable training with standard reinforcement learning frameworks designed for much simpler environments. Neural MMO 2.0 is free and open-source with comprehensive documentation available at neuralmmo.github.io

In this work, we improve on the upper and lower bounds for the regret of online learning with strongly observable undirected feedback graphs. The best known upper bound for this problem is $\mathcal{O}\bigl(\sqrt{\alpha T\ln K}\bigr)$, where $K$ is the number of actions, $\alpha$ is the independence number of the graph, and $T$ is the time horizon. The $\sqrt{\ln K}$ factor is known to be necessary when $\alpha = 1$ (the experts case). On the other hand, when $\alpha = K$ (the bandits case), the minimax rate is known to be $\Theta\bigl(\sqrt{KT}\bigr)$, and a lower bound $\Omega\bigl(\sqrt{\alpha T}\bigr)$ is known to hold for any $\alpha$. Our improved upper bound $\mathcal{O}\bigl(\sqrt{\alpha T(1+\ln(K/\alpha))}\bigr)$ holds for any $\alpha$ and matches the lower bounds for bandits and experts, while interpolating intermediate cases.

Lifelong learning offers a promising paradigm of building a generalist agent that learns and adapts over its lifespan. Unlike traditional lifelong learning problems in image and text domains, which primarily involve the transfer of declarative knowledge of entities and concepts, lifelong learning in decision-making (LLDM) also necessitates the transfer of procedural knowledge, such as actions and behaviors. To advance research in LLDM, we introduce LIBERO, a novel benchmark of lifelong learning for robot manipulation. Specifically, LIBERO highlights five key research topics in LLDM: 1) how to efficiently transfer declarative knowledge, procedural knowledge, or the mixture of both; 2) how to design effective policy architectures and 3) effective algorithms for LLDM; 4) the robustness of a lifelong learner with respect to task ordering; and 5) the effect of model pretraining for LLDM. We develop an extendible procedural generation pipeline that can in principle generate infinitely many tasks. For benchmarking purpose, we create four task suites (130 tasks in total) that we use to investigate the above-mentioned research topics. To support sample-efficient learning, we provide high-quality human-teleoperated demonstration data for all tasks. Our extensive experiments present several insightful or even unexpected discoveries: sequential finetuning outperforms existing lifelong learning methods in forward transfer, no single visual encoder architecture excels at all types of knowledge transfer, and naive supervised pretraining can hinder agents' performance in the subsequent LLDM.

In this work, we aim to characterize the statistical complexity of realizable regression both in the PAC learning setting and the online learning setting. Previous work had established the sufficiency of finiteness of the fat shattering dimension for PAC learnability and the necessity of finiteness of the scaled Natarajan dimension, but little progress had been made towards a more complete characterization since the work of Simon 1997 (SICOMP '97). To this end, we first introduce a minimax instance optimal learner for realizable regression and propose a novel dimension that both qualitatively and quantitatively characterizes which classes of real-valued predictors are learnable. We then identify a combinatorial dimension related to the graph dimension that characterizes ERM learnability in the realizable setting. Finally, we establish a necessary condition for learnability based on a combinatorial dimension related to the DS dimension, and conjecture that it may also be sufficient in this context. Additionally, in the context of online learning we provide a dimension that characterizes the minimax instance optimal cumulative loss up to a constant factor and design an optimal online learner for realizable regression, thus resolving an open question raised by Daskalakis and Golowich in STOC '22.

Model distillation is frequently proposed as a technique to reduce the privacy leakage of machine learning. These empirical privacy defenses rely on the intuition that distilled teacher'' model. In this work, we design membership inference attacks to systematically study the privacy provided by knowledge distillation to both the teacher and student training sets. Our new attacks show that distillation alone provides only limited privacy across a number of domains. We explain the success of our attacks on distillation by showing that membership inference attacks on a private dataset can succeed even if the target model is never queried on any actual training points, but only on inputs whose predictions are highly influenced by training data. Finally, we show that our attacks are strongest when student and teacher sets are similar, or when the attacker can poison the teacher set.