OpenRaiser/Intern-Atlas huggingface dataset:
The Logical Options Framework
Venue: Conference ICML 2021
Year: 2021

Learning composable policies for environments with complex rules and tasks is a challenging problem. We introduce a hierarchical reinforcement learning framework called the Logical Options Framework (LOF) that learns policies that are satisfying, optimal, and composable. LOF efficiently learns policies that satisfy tasks by representing the task as an automaton and integrating it into learning and planning. We provide and prove conditions under which LOF will learn satisfying, optimal policies. And lastly, we show how LOF's learned policies can be composed to satisfy unseen tasks with only 10-50 retraining steps. We evaluate LOF on four tasks in discrete and continuous domains, including a 3D pick-and-place environment.
Analyzing the tree-layer structure of Deep Forests
Venue: Conference ICML 2021
Year: 2021

Random forests on the one hand, and neural networks on the other hand, have met great success in the machine learning community for their predictive performance. Combinations of both have been proposed in the literature, notably leading to the so-called deep forests (DF) (Zhou \& Feng,2019). In this paper, our aim is not to benchmark DF performances but to investigate instead their underlying mechanisms. Additionally, DF architecture can be generally simplified into more simple and computationally efficient shallow forest networks. Despite some instability, the latter may outperform standard predictive tree-based methods. We exhibit a theoretical framework in which a shallow tree network is shown to enhance the performance of classical decision trees. In such a setting, we provide tight theoretical lower and upper bounds on its excess risk. These theoretical results show the interest of tree-network architectures for well-structured data provided that the first layer, acting as a data encoder, is rich enough.
Deciding What to Learn: A Rate-Distortion Approach
Venue: Conference ICML 2021
Year: 2021

Agents that learn to select optimal actions represent a prominent focus of the sequential decision-making literature. In the face of a complex environment or constraints on time and resources, however, aiming to synthesize such an optimal policy can become infeasible. These scenarios give rise to an important trade-off between the information an agent must acquire to learn and the sub-optimality of the resulting policy. While an agent designer has a preference for how this trade-off is resolved, existing approaches further require that the designer translate these preferences into a fixed learning target for the agent. In this work, leveraging rate-distortion theory, we automate this process such that the designer need only express their preferences via a single hyperparameter and the agent is endowed with the ability to compute its own learning targets that best achieve the desired trade-off. We establish a general bound on expected discounted regret for an agent that decides what to learn in this manner along with computational experiments that illustrate the expressiveness of designer preferences and even show improvements over Thompson sampling in identifying an optimal policy.
Private Adaptive Gradient Methods for Convex Optimization
Venue: Conference ICML 2021
Year: 2021

We study adaptive methods for differentially private convex optimization, proposing and analyzing differentially private variants of a Stochastic Gradient Descent (SGD) algorithm with adaptive stepsizes, as well as the AdaGrad algorithm. We provide upper bounds on the regret of both algorithms and show that the bounds are (worst-case) optimal. As a consequence of our development, we show that our private versions of AdaGrad outperform adaptive SGD, which in turn outperforms traditional SGD in scenarios with non-isotropic gradients where (non-private) Adagrad provably outperforms SGD. The major challenge is that the isotropic noise typically added for privacy dominates the signal in gradient geometry for high-dimensional problems; approaches to this that effectively optimize over lower-dimensional subspaces simply ignore the actual problems that varying gradient geometries introduce. In contrast, we study non-isotropic clipping and noise addition, developing a principled theoretical approach; the consequent procedures also enjoy significantly stronger empirical performance than prior approaches.
Combinatorial Blocking Bandits with Stochastic Delays
Venue: Conference ICML 2021
Year: 2021

Recent work has considered natural variations of the multi-armed bandit problem, where the reward distribution of each arm is a special function of the time passed since its last pulling. In this direction, a simple (yet widely applicable) model is that of blocking bandits, where an arm becomes unavailable for a deterministic number of rounds after each play. In this work, we extend the above model in two directions: (i) We consider the general combinatorial setting where more than one arms can be played at each round, subject to feasibility constraints. (ii) We allow the blocking time of each arm to be stochastic. We first study the computational/unconditional hardness of the above setting and identify the necessary conditions for the problem to become tractable (even in an approximate sense). Based on these conditions, we provide a tight analysis of the approximation guarantee of a natural greedy heuristic that always plays the maximum expected reward feasible subset among the available (non-blocked) arms. When the arms' expected rewards are unknown, we adapt the above heuristic into a bandit algorithm, based on UCB, for which we provide sublinear (approximate) regret guarantees, matching the theoretical lower bounds in the limiting case of absence of delays.
Decomposable Submodular Function Minimization via Maximum Flow
Venue: Conference ICML 2021
Year: 2021

This paper bridges discrete and continuous optimization approaches for decomposable submodular function minimization, in both the standard and parametric settings. We provide improved running times for this problem by reducing it to a number of calls to a maximum flow oracle. When each function in the decomposition acts on $O(1)$ elements of the ground set $V$ and is polynomially bounded, our running time is up to polylogarithmic factors equal to that of solving maximum flow in a sparse graph with $O(\vert V \vert)$ vertices and polynomial integral capacities. We achieve this by providing a simple iterative method which can optimize to high precision any convex function defined on the submodular base polytope, provided we can efficiently minimize it on the base polytope corresponding to the cut function of a certain graph that we construct. We solve this minimization problem by lifting the solutions of a parametric cut problem, which we obtain via a new efficient combinatorial reduction to maximum flow. This reduction is of independent interest and implies some previously unknown bounds for the parametric minimum $s,t$-cut problem in multiple settings.
Differentially Private Query Release Through Adaptive Projection
Venue: Conference ICML 2021
Year: 2021

We propose, implement, and evaluate a new algorithm for releasing answers to very large numbers of statistical queries like $k$-way marginals, subject to differential privacy. Our algorithm makes adaptive use of a continuous relaxation of the Projection Mechanism, which answers queries on the private dataset using simple perturbation, and then attempts to find the synthetic dataset that most closely matches the noisy answers. We use a continuous relaxation of the synthetic dataset domain which makes the projection loss differentiable, and allows us to use efficient ML optimization techniques and tooling. Rather than answering all queries up front, we make judicious use of our privacy budget by iteratively and adaptively finding queries for which our (relaxed) synthetic data has high error, and then repeating the projection. We perform extensive experimental evaluations across a range of parameters and datasets, and find that our method outperforms existing algorithms in many cases, especially when the privacy budget is small or the query class is large.
On the Implicit Bias of Initialization Shape: Beyond Infinitesimal Mirror Descent
Venue: Conference ICML 2021
Year: 2021

Recent work has highlighted the role of initialization scale in determining the structure of the solutions that gradient methods converge to. In particular, it was shown that large initialization leads to the neural tangent kernel regime solution, whereas small initialization leads to so called "rich regimes". However, the initialization structure is richer than the overall scale alone and involves relative magnitudes of different weights and layers in the network. Here we show that these relative scales, which we refer to as initialization shape, play an important role in determining the learned model. We develop a novel technique for deriving the inductive bias of gradient-flow and use it to obtain closed-form implicit regularizers for multiple cases of interest.
On-Off Center-Surround Receptive Fields for Accurate and Robust Image Classification
Venue: Conference ICML 2021
Year: 2021

Robustness to variations in lighting conditions is a key objective for any deep vision system. To this end, our paper extends the receptive field of convolutional neural networks with two residual components, ubiquitous in the visual processing system of vertebrates: On-center and off-center pathways, with excitatory center and inhibitory surround; OOCS for short. The on-center pathway is excited by the presence of a light stimulus in its center but not in its surround, whereas the off-center one is excited by the absence of a light stimulus in its center but not in its surround. We design OOCS pathways via a difference of Gaussians, with their variance computed analytically from the size of the receptive fields. OOCS pathways complement each other in their response to light stimuli, ensuring this way a strong edge-detection capability, and as a result, an accurate and robust inference under challenging lighting conditions. We provide extensive empirical evidence showing that networks supplied with the OOCS edge representation gain accuracy and illumination-robustness compared to standard deep models.
Uniform Convergence, Adversarial Spheres and a Simple Remedy
Venue: Conference ICML 2021
Year: 2021

Previous work has cast doubt on the general framework of uniform convergence and its ability to explain generalization in neural networks. By considering a specific dataset, it was observed that a neural network completely misclassifies a projection of the training data (adversarial set), rendering any existing generalization bound based on uniform convergence vacuous. We provide an extensive theoretical investigation of the previously studied data setting through the lens of infinitely-wide models. We prove that the Neural Tangent Kernel (NTK) also suffers from the same phenomenon and we uncover its origin. We highlight the important role of the output bias and show theoretically as well as empirically how a sensible choice completely mitigates the problem. We identify sharp phase transitions in the accuracy on the adversarial set and study its dependency on the training sample size. As a result, we are able to characterize critical sample sizes beyond which the effect disappears. Moreover, we study decompositions of a neural network into a clean and noisy part by considering its canonical decomposition into its different eigenfunctions and show empirically that for too small bias the adversarial phenomenon still persists.
Faster Kernel Matrix Algebra via Density Estimation
Venue: Conference ICML 2021
Year: 2021

We study fast algorithms for computing fundamental properties of a positive semidefinite kernel matrix $K \in \mathbb{R}^{n \times n}$ corresponding to $n$ points $x_1,\ldots,x_n \in \mathbb{R}^d$. In particular, we consider estimating the sum of kernel matrix entries, along with its top eigenvalue and eigenvector. We show that the sum of matrix entries can be estimated to $1+ε$ relative error in time $sublinear$ in $n$ and linear in $d$ for many popular kernels, including the Gaussian, exponential, and rational quadratic kernels. For these kernels, we also show that the top eigenvalue (and an approximate eigenvector) can be approximated to $1+ε$ relative error in time $subquadratic$ in $n$ and linear in $d$. Our algorithms represent significant advances in the best known runtimes for these problems. They leverage the positive definiteness of the kernel matrix, along with a recent line of work on efficient kernel density estimation.
Robust Reinforcement Learning using Least Squares Policy Iteration with Provable Performance Guarantees
Venue: Conference ICML 2021
Year: 2021

This paper addresses the problem of model-free reinforcement learning for Robust Markov Decision Process (RMDP) with large state spaces. The goal of the RMDP framework is to find a policy that is robust against the parameter uncertainties due to the mismatch between the simulator model and real-world settings. We first propose the Robust Least Squares Policy Evaluation algorithm, which is a multi-step online model-free learning algorithm for policy evaluation. We prove the convergence of this algorithm using stochastic approximation techniques. We then propose Robust Least Squares Policy Iteration (RLSPI) algorithm for learning the optimal robust policy. We also give a general weighted Euclidean norm bound on the error (closeness to optimality) of the resulting policy. Finally, we demonstrate the performance of our RLSPI algorithm on some standard benchmark problems.
How Important is the Train-Validation Split in Meta-Learning?
Venue: Conference ICML 2021
Year: 2021

Meta-learning aims to perform fast adaptation on a new task through learning a "prior" from multiple existing tasks. A common practice in meta-learning is to perform a train-validation split (\emph{train-val method}) where the prior adapts to the task on one split of the data, and the resulting predictor is evaluated on another split. Despite its prevalence, the importance of the train-validation split is not well understood either in theory or in practice, particularly in comparison to the more direct \emph{train-train method}, which uses all the per-task data for both training and evaluation. We provide a detailed theoretical study on whether and when the train-validation split is helpful in the linear centroid meta-learning problem. In the agnostic case, we show that the expected loss of the train-val method is minimized at the optimal prior for meta testing, and this is not the case for the train-train method in general without structural assumptions on the data. In contrast, in the realizable case where the data are generated from linear models, we show that both the train-val and train-train losses are minimized at the optimal prior in expectation. Further, perhaps surprisingly, our main result shows that the train-train method achieves a \emph{strictly better} excess loss in this realizable case, even when the regularization parameter and split ratio are optimally tuned for both methods. Our results highlight that sample splitting may not always be preferable, especially when the data is realizable by the model. We validate our theories by experimentally showing that the train-train method can indeed outperform the train-val method, on both simulations and real meta-learning tasks.
Stabilizing Equilibrium Models by Jacobian Regularization
Venue: Conference ICML 2021
Year: 2021

Deep equilibrium networks (DEQs) are a new class of models that eschews traditional depth in favor of finding the fixed point of a single nonlinear layer. These models have been shown to achieve performance competitive with the state-of-the-art deep networks while using significantly less memory. Yet they are also slower, brittle to architectural choices, and introduce potential instability to the model. In this paper, we propose a regularization scheme for DEQ models that explicitly regularizes the Jacobian of the fixed-point update equations to stabilize the learning of equilibrium models. We show that this regularization adds only minimal computational cost, significantly stabilizes the fixed-point convergence in both forward and backward passes, and scales well to high-dimensional, realistic domains (e.g., WikiText-103 language modeling and ImageNet classification). Using this method, we demonstrate, for the first time, an implicit-depth model that runs with approximately the same speed and level of performance as popular conventional deep networks such as ResNet-101, while still maintaining the constant memory footprint and architectural simplicity of DEQs. Code is available at https://github.com/locuslab/deq .
Principled Exploration via Optimistic Bootstrapping and Backward Induction
Venue: Conference ICML 2021
Year: 2021

One principled approach for provably efficient exploration is incorporating the upper confidence bound (UCB) into the value function as a bonus. However, UCB is specified to deal with linear and tabular settings and is incompatible with Deep Reinforcement Learning (DRL). In this paper, we propose a principled exploration method for DRL through Optimistic Bootstrapping and Backward Induction (OB2I). OB2I constructs a general-purpose UCB-bonus through non-parametric bootstrap in DRL. The UCB-bonus estimates the epistemic uncertainty of state-action pairs for optimistic exploration. We build theoretical connections between the proposed UCB-bonus and the LSVI-UCB in a linear setting. We propagate future uncertainty in a time-consistent manner through episodic backward update, which exploits the theoretical advantage and empirically improves the sample-efficiency. Our experiments in the MNIST maze and Atari suite suggest that OB2I outperforms several state-of-the-art exploration approaches.
GLSearch: Maximum Common Subgraph Detection via Learning to Search
Venue: Conference ICML 2021
Year: 2021

Detecting the Maximum Common Subgraph (MCS) between two input graphs is fundamental for applications in drug synthesis, malware detection, cloud computing, etc. However, MCS computation is NP-hard, and state-of-the-art MCS solvers rely on heuristic search algorithms which in practice cannot find good solution for large graph pairs given a limited computation budget. We propose GLSearch, a Graph Neural Network (GNN) based learning to search model. Our model is built upon the branch and bound algorithm, which selects one pair of nodes from the two input graphs to expand at a time. Instead of using heuristics, we propose a novel GNN-based Deep Q-Network (DQN) to select the node pair, allowing the search process faster and more adaptive. To further enhance the training of DQN, we leverage the search process to provide supervision in a pre-training stage and guide our agent during an imitation learning stage. Experiments on synthetic and real-world large graph pairs demonstrate that our model learns a search strategy that is able to detect significantly larger common subgraphs given the same computation budget. Our GLSearch can be potentially extended to solve many other combinatorial problems with constraints on graphs.
Breaking the Limits of Message Passing Graph Neural Networks
Venue: Conference ICML 2021
Year: 2021

Since the Message Passing (Graph) Neural Networks (MPNNs) have a linear complexity with respect to the number of nodes when applied to sparse graphs, they have been widely implemented and still raise a lot of interest even though their theoretical expressive power is limited to the first order Weisfeiler-Lehman test (1-WL). In this paper, we show that if the graph convolution supports are designed in spectral-domain by a non-linear custom function of eigenvalues and masked with an arbitrary large receptive field, the MPNN is theoretically more powerful than the 1-WL test and experimentally as powerful as a 3-WL existing models, while remaining spatially localized. Moreover, by designing custom filter functions, outputs can have various frequency components that allow the convolution process to learn different relationships between a given input graph signal and its associated properties. So far, the best 3-WL equivalent graph neural networks have a computational complexity in $\mathcal{O}(n^3)$ with memory usage in $\mathcal{O}(n^2)$, consider non-local update mechanism and do not provide the spectral richness of output profile. The proposed method overcomes all these aforementioned problems and reaches state-of-the-art results in many downstream tasks.
Instance Specific Approximations for Submodular Maximization
Venue: Conference ICML 2021
Year: 2021

For many optimization problems in machine learning, finding an optimal solution is computationally intractable and we seek algorithms that perform well in practice. Since computational intractability often results from pathological instances, we look for methods to benchmark the performance of algorithms against optimal solutions on real-world instances. The main challenge is that an optimal solution cannot be efficiently computed for intractable problems, and we therefore often do not know how far a solution is from being optimal. A major question is therefore how to measure the performance of an algorithm in comparison to an optimal solution on instances we encounter in practice. In this paper, we address this question in the context of submodular optimization problems. For the canonical problem of submodular maximization under a cardinality constraint, it is intractable to compute a solution that is better than a $1-1/e \approx 0.63$ fraction of the optimum. Algorithms like the celebrated greedy algorithm are guaranteed to achieve this $1-1/e$ bound on any instance and are used in practice. Our main contribution is not a new algorithm for submodular maximization but an analytical method that measures how close an algorithm for submodular maximization is to optimal on a given problem instance. We use this method to show that on a wide variety of real-world datasets and objectives, the approximation of the solution found by greedy goes well beyond $1-1/e$ and is often at least 0.95. We develop this method using a novel technique that lower bounds the objective of a dual minimization problem to obtain an upper bound on the value of an optimal solution to the primal maximization problem.
Augmented World Models Facilitate Zero-Shot Dynamics Generalization From a Single Offline Environment
Venue: Conference ICML 2021
Year: 2021

Reinforcement learning from large-scale offline datasets provides us with the ability to learn policies without potentially unsafe or impractical exploration. Significant progress has been made in the past few years in dealing with the challenge of correcting for differing behavior between the data collection and learned policies. However, little attention has been paid to potentially changing dynamics when transferring a policy to the online setting, where performance can be up to 90% reduced for existing methods. In this paper we address this problem with Augmented World Models (AugWM). We augment a learned dynamics model with simple transformations that seek to capture potential changes in physical properties of the robot, leading to more robust policies. We not only train our policy in this new setting, but also provide it with the sampled augmentation as a context, allowing it to adapt to changes in the environment. At test time we learn the context in a self-supervised fashion by approximating the augmentation which corresponds to the new environment. We rigorously evaluate our approach on over 100 different changed dynamics settings, and show that this simple approach can significantly improve the zero-shot generalization of a recent state-of-the-art baseline, often achieving successful policies where the baseline fails.