Much of the work in online learning focuses on the study of sublinear upper bounds on the regret. In this work, we initiate the study of best-case lower bounds in online convex optimization, wherein we bound the largest \emph{improvement} an algorithm can obtain relative to the single best action in hindsight. This problem is motivated by the goal of better understanding the adaptivity of a learning algorithm. Another motivation comes from fairness: it is known that best-case lower bounds are instrumental in obtaining algorithms for decision-theoretic online learning (DTOL) that satisfy a notion of group fairness. Our contributions are a general method to provide best-case lower bounds in Follow The Regularized Leader (FTRL) algorithms with time-varying regularizers, which we use to show that best-case lower bounds are of the same order as existing upper regret bounds: this includes situations with a fixed learning rate, decreasing learning rates, timeless methods, and adaptive gradient methods. In stark contrast, we show that the linearized version of FTRL can attain negative linear regret. Finally, in DTOL with two experts and binary losses, we fully characterize the best-case sequences, which provides a finer understanding of the best-case lower bounds.

Hierarchical reinforcement learning (HRL) holds great potential for sample-efficient learning on challenging long-horizon tasks. In particular, letting a higher level assign subgoals to a lower level has been shown to enable fast learning on difficult problems. However, such subgoal-based methods have been designed with static reinforcement learning environments in mind and consequently struggle with dynamic elements beyond the immediate control of the agent even though they are ubiquitous in real-world problems. In this paper, we introduce Hierarchical reinforcement learning with Timed Subgoals (HiTS), an HRL algorithm that enables the agent to adapt its timing to a dynamic environment by not only specifying what goal state is to be reached but also when. We discuss how communicating with a lower level in terms of such timed subgoals results in a more stable learning problem for the higher level. Our experiments on a range of standard benchmarks and three new challenging dynamic reinforcement learning environments show that our method is capable of sample-efficient learning where an existing state-of-the-art subgoal-based HRL method fails to learn stable solutions.

High dimensional black-box optimization has broad applications but remains a challenging problem to solve. Given a set of samples x i, building a global model (like Bayesian Optimization (BO)) suffers from the curse of dimensionality in the high-dimensional search space, while a greedy search may lead to sub-optimality. By recursively splitting the search space into regions with high/low function values, recent works like LaNAS shows good performance in Neural Architecture Search (NAS), reducing the sample complexity empirically. In this paper, we coin LA-MCTS that extends LaNAS to other domains. Unlike previous approaches, LA-MCTS learns the partition of the search space using a few samples and their function values in an online fashion. While LaNAS uses linear partition and performs uniform sampling in each region, our LA-MCTS adopts a nonlinear decision boundary and learns a local model to pick good candidates. If the nonlinear partition function and the local model fits well with ground-truth black-box function, then good partitions and candidates can be reached with much fewer samples. LA-MCTS serves as a meta-algorithm by using existing black-box optimizers (e.g., BO, TuRBO as its local models, achieving strong performance in general black-box optimization and reinforcement learning benchmarks, in particular for high-dimensional problems.

One of the most effective continuous deep reinforcement learning algorithms is normalized advantage functions (NAF). The main idea of NAF consists in the approximation of the Q-function by functions quadratic with respect to the action variable. This idea allows to apply the algorithm to continuous reinforcement learning problems, but on the other hand, it brings up the question of classes of problems in which this approximation is acceptable. The presented paper describes one such class. We consider reinforcement learning problems obtained by the discretization of certain optimal control problems. Based on the idea of NAF, we present a new family of quadratic functions and prove its suitable approximation properties. Taking these properties into account, we provide several ways to improve NAF. The experimental results confirm the efficiency of our improvements.

We introduce a new and completely online contextual bandit algorithm called Gated Linear Contextual Bandits (GLCB). This algorithm is based on Gated Linear Networks (GLNs), a recently introduced deep learning architecture with properties well-suited to the online setting. Leveraging data-dependent gating properties of the GLN we are able to estimate prediction uncertainty with effectively zero algorithmic overhead. We empirically evaluate GLCB compared to 9 state-of-the-art algorithms that leverage deep neural networks, on a standard benchmark suite of discrete and continuous contextual bandit problems. GLCB obtains mean first-place despite being the only online method, and we further support these results with a theoretical study of its convergence properties.

How do we build unified models that apply across multiple environments? We propose the multi-environment Symbolic Interactive Language Grounding benchmark (SILG), which unifies a collection of diverse grounded language learning environments under a common interface. SILG consists of grid-world environments that require generalization to new dynamics, entities, and partially observed worlds (RTFM, Messenger, NetHack), as well as symbolic counterparts of visual worlds that require interpreting rich natural language with respect to complex scenes (ALFWorld, Touchdown). Together, these environments provide diverse grounding challenges in richness of observation space, action space, language specification, and plan complexity. In addition, we propose the first shared model architecture for RL on these environments, and evaluate recent advances such as egocentric local convolution, recurrent state-tracking, entity-centric attention, and pretrained LM using SILG.

Humans learn from visual inputs at multiple timescales, both rapidly and flexibly acquiring visual knowledge over short periods, and robustly accumulating online learning progress over longer periods. Modeling these powerful learning capabilities is an important problem for computational visual cognitive science, and models that could replicate them would be of substantial utility in real-world computer vision settings. In this work, we establish benchmarks for both real-time and life-long continual visual learning. Our real-time learning benchmark measures a model's ability to match the rapid visual behavior changes of real humans over the course of minutes and hours, given a stream of visual inputs. Our life-long learning benchmark evaluates the performance of models in a purely online learning curriculum obtained directly from child visual experience over the course of years of development.

To obtain excellent deep neural architectures, a series of techniques are carefully designed in EfficientNets. The giant formula for simultaneously enlarging the resolution, depth and width provides us a Rubik's cube for neural networks. So that we can find networks with high efficiency and excellent performance by twisting the three dimensions. This paper aims to explore the twisting rules for obtaining deep neural networks with minimum model sizes and computational costs. Different from the network enlarging, we observe that resolution and depth are more important than width for tiny networks. Therefore, the original method, \ie the compound scaling in EfficientNet is no longer suitable. To this end, we summarize a tiny formula for downsizing neural architectures through a series of smaller models derived from the EfficientNet-B0 with the FLOPs constraint. Experimental results on the ImageNet benchmark illustrate that our TinyNet performs much better than the smaller version of EfficientNets using the inversed giant formula. For instance, our TinyNet-E achieves a 59.9\% Top-1 accuracy with only 24M FLOPs, which is about 1.9\% higher than that of the previous best MobileNetV3 with similar computational cost.

Personalized PageRank (PPR) is a fundamental tool in unsupervised learning of graph representations such as node ranking, labeling, and graph embedding. However, while data privacy is one of the most important recent concerns, existing PPR algorithms are not designed to protect user privacy. PPR is highly sensitive to the input graph edges: the difference of only one edge may cause a big change in the PPR vector, potentially leaking private user data.In this work, we propose an algorithm which outputs an approximate PPR and has provably bounded sensitivity to input edges. In addition, we prove that our algorithm achieves similar accuracy to non-private algorithms when the input graph has large degrees. Our sensitivity-bounded PPR directly implies private algorithms for several tools of graph learning, such as, differentially private (DP) PPR ranking, DP node classification, and DP node embedding. To complement our theoretical analysis, we also empirically verify the practical performances of our algorithms.

In this paper, we propose an end-to-end graph learning framework, namely \textbf{I}terative \textbf{D}eep \textbf{G}raph \textbf{L}earning (\alg), for jointly and iteratively learning graph structure and graph embedding. The key rationale of \alg is to learn a better graph structure based on better node embeddings, and vice versa (i.e., better node embeddings based on a better graph structure). Our iterative method dynamically stops when the learned graph structure approaches close enough to the graph optimized for the downstream prediction task. In addition, we cast the graph learning problem as a similarity metric learning problem and leverage adaptive graph regularization for controlling the quality of the learned graph. Finally, combining the anchor-based approximation technique, we further propose a scalable version of \alg, namely \salg, which significantly reduces the time and space complexity of \alg without compromising the performance. Our extensive experiments on nine benchmarks show that our proposed \alg models can consistently outperform or match the state-of-the-art baselines. Furthermore, \alg can be more robust to adversarial graphs and cope with both transductive and inductive learning.