Amii research at the International Conference on Machine Learning 2023

This year marks the 40th year of the International Conference on Machine Learning (ICML), and Amii’s researchers and students are presenting their research at this year’s event.

ICML, which runs from July 23 - 29 in Hawaii this year, is the premier gathering of professionals dedicated to the advancement of the branch of AI known as machine learning (ML). Globally renowned for presenting and publishing cutting-edge research on all aspects of ML and application areas, the conference is within the top ten highest-ranked ML & AI conferences in the world based on h-index and Impact Score values.

Check out some of the leading-edge research being presented by Amii scientists.

Bolded names denote Amii students, fellows and staff

Toward Efficient Gradient-Based Value Estimation

Arsalan Sharifnassab, Richard Sutton

Abstract: Gradient-based methods for value estimation in reinforcement learning have favorable stability properties, but they are typically much slower than Temporal Difference (TD) learning methods. We study the root causes of this slowness and show that Mean Square Bellman Error (MSBE) is an ill-conditioned loss function in the sense that its Hessian has large condition-number. To resolve the adverse effect of poor conditioning of MSBE on gradient based methods, we propose a low complexity batch-free proximal method that approximately follows the Gauss-Newton direction and is asymptotically robust to parameterization. Our main algorithm, called RANS, is efficient in the sense that it is significantly faster than the residual gradient methods while having almost the same computational complexity, and is competitive with TD on the classic problems that we tested.

Settling the Reward Hypothesis

Michael Bowling, John D. Martin, David Abel, Will Dabney

Abstract: The reward hypothesis posits that, "all of what we mean by goals and purposes can be well thought of as maximization of the expected value of the cumulative sum of a received scalar signal (reward)." We aim to fully settle this hypothesis. This will not conclude with a simple affirmation or refutation, but rather specify completely the implicit requirements on goals and purposes under which the hypothesis holds.

An Effective Meaningful Way to Evaluate Survival Models

Shi-ang Qi, Neeraj Kumar, Mahtab Farrokh, Weijie Sun, Li-Hao Kuan, Rajesh Ranganath, Ricardo Henao, Russell Greiner

Abstract: One straightforward metric to evaluate a survival prediction model is based on the Mean Absolute Error (MAE) -- the average of the absolute difference between the time predicted by the model and the true event time, over all subjects. Unfortunately, this is challenging because, in practice, the test set includes (right) censored individuals, meaning we do not know when a censored individual actually experienced the event. In this paper, we explore various metrics to estimate MAE for survival datasets that include (many) censored individuals. Moreover, we introduce a novel and effective approach for generating realistic semi-synthetic survival datasets to facilitate the evaluation of metrics. Our findings, based on the analysis of the semi-synthetic datasets, reveal that our proposed metric (MAE using pseudo-observations) is able to rank models accurately based on their performance, and often closely matches the true MAE -- in particular, is better than several alternative methods.

Formalizing Preferences Over Runtime Distributions

Devon R. Graham, Kevin Leyton-Brown, Tim Roughgarden

Abstract: When trying to solve a computational problem, we are often faced with a choice between algorithms that are guaranteed to return the right answer but differ in their runtime distributions (e.g., SAT solvers, sorting algorithms). This paper aims to lay theoretical foundations for such choices by formalizing preferences over runtime distributions. It might seem that we should simply prefer the algorithm that minimizes expected runtime. However, such preferences would be driven by exactly how slow our algorithm is on bad inputs, whereas in practice we are typically willing to cut off occasional, sufficiently long runs before they finish. We propose a principled alternative, taking a utility-theoretic approach to characterize the scoring functions that describe preferences over algorithms. These functions depend on the way our value for solving our problem decreases with time and on the distribution from which captimes are drawn. We describe examples of realistic utility functions and show how to leverage a maximum-entropy approach for modeling underspecified captime distributions. Finally, we show how to efficiently estimate an algorithm's expected utility from runtime samples.

Deep Laplacian-based Options for Temporally-Extended Exploration

Martin Klissarov, Marlos C. Machado

Abstract: Selecting exploratory actions that generate a rich stream of experience for better learning is a fundamental challenge in reinforcement learning (RL). An approach to tackle this problem consists in selecting actions according to specific policies for an extended period of time, also known as options. A recent line of work to derive such exploratory options builds upon the eigenfunctions of the graph Laplacian. Importantly, until now these methods have been mostly limited to tabular domains where (1) the graph Laplacian matrix was either given or could be fully estimated, (2) performing eigendecomposition on this matrix was computationally tractable, and (3) value functions could be learned exactly. Additionally, these methods required a separate option discovery phase. These assumptions are fundamentally not scalable. In this paper we address these limitations and show how recent results for directly approximating the eigenfunctions of the Laplacian can be leveraged to truly scale up options-based exploration. To do so, we introduce a fully online deep RL algorithm for discovering Laplacian-based options and evaluate our approach on a variety of pixel-based tasks. We compare to several state-of-the-art exploration methods and show that our approach is effective, general, and especially promising in non-stationary settings.

Correcting discount-factor mismatch in on-policy policy gradient methods

Fengdi Che, Gautham Vasan, A. Rupam Mahmood

Abstract: The policy gradient theorem gives a convenient form of the policy gradient in terms of three factors: an action value, a gradient of the action likelihood, and a state distribution involving discounting called the discounted stationary distribution. But commonly used on-policy methods based on the policy gradient theorem ignores the discount factor in the state distribution, which is technically incorrect and may even cause degenerate learning behavior in some environments. An existing solution corrects this discrepancy by using γ as a factor in the gradient estimate. However, this solution is not widely adopted and does not work well in tasks where the later states are similar to earlier states. We introduce a novel distribution correction to account for the discounted stationary distribution that can be plugged into many existing gradient estimators. Our correction circumvents the performance degradation associated with the γ correction with a lower variance. Importantly, compared to the uncorrected estimators, our algorithm provides improved state emphasis to evade suboptimal policies in certain environments and consistently matches or exceeds the original performance on several OpenAI gym and DeepMind suite benchmarks.

Target-based Surrogates for Stochastic Optimization

Jonathan Wilder Lavington, Sharan Vaswani, Reza Babanezhad, Mark Schmidt, Nicolas Le Roux

Abstract: We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a \emph{target space} (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the SSO algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for SSO when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of SSO.

Let's Make Block Coordinate Descent Converge Faster: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence

Julie Nutini, Issam Laradji, Mark Schmidt

Abstract: Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can significantly improve the progress made by each BCD iteration. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with sparse dependencies between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active-set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization.

Simplifying Momentum-based Positive-definite Submanifold Optimization with Applications to Deep Learning

Wu Lin, Valentin Duruisseaux, Melvin Leok, Frank Nielsen, Mohammad Emtiyaz Khan, Mark Schmidt

Abstract: Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties for a class of structured symmetric positive-definite matrices with the affine-invariant metric. We do so by proposing a generalized version of the Riemannian normal coordinates that dynamically orthonormalizes the metric and locally converts the problem into an unconstrained problem in the Euclidean space. We use our approach to simplify existing approaches for structured covariances and develop matrix-inverse-free 2nd-order optimizers for deep learning with low precision by using only matrix multiplications.

Gradient-Free Structured Pruning with Unlabeled Data

Azade Nova, Hanjun Dai, Dale Schuurmans

Abstract: Large Language Models (LLMs) have achieved great success in solving difficult tasks across many domains, but such success comes with a high computation cost, and inference latency. As developers and third parties customize these models, the need to provide efficient inference has increased. Many efforts have attempted to reduce inference cost through model compression techniques such as pruning and distillation. However, these techniques either require labeled data, or are time-consuming as they require the compressed model to be retrained to regain accuracy. In this paper, we propose a gradient-free structured pruning framework that uses only unlabeled data. An evaluation on the GLUE and SQuAD benchmarks using BERTBASE and DistilBERT illustrates the effectiveness of the proposed approach. By only using the weights of the pre-trained model and unlabeled data, in a matter of a few minutes on a single GPU, up to 40% of the original FLOP count can be reduced with less than a 4% accuracy loss across all tasks considered.

Revisiting Sampling for Combinatorial Optimization

Haoran Sun, Katayoon Goshvadi, Azade Nova, Dale Schuurmans, Hanjun Dai

Abstract: Sampling approaches like Markov chain Monte Carlo were once popular for combinatorial optimization, but the inefficiency of classical methods and the need for problem-specific designs curtailed ongoing development. Recent work has favored data-driven approaches that mitigate the need for hand-craft heuristics, but these are often not usable as out-of-the-box solvers due to dependence on in-distribution training and limited scalability to large instances. In this paper, we revisit the idea of using sampling for combinatorial optimization, motivated by the significant recent advances of gradient-based discrete MCMC and new techniques for parallel neighborhood exploration on accelerators. Remarkably, we find that modern sampling strategies can leverage landscape information to provide general-purpose solvers that require no training and yet are competitive with state of the art combinatorial solvers. In particular, experiments on cover vertex selection, graph partition and routing demonstrate better speed-quality trade-offs over current learning based approaches, and sometimes even superior performance to commercial solvers and specialized algorithms.

Stochastic Gradient Succeeds for Bandits

Jincheng Mei, Zixin Zhong, Bo Dai, Alekh Agarwal, Csaba Szepesvari, Dale Schuurmans

Abstract: We show that the stochastic gradient bandit algorithm converges to a globally optimal policy at an O(1/t) rate, even with a constant step size. Remarkably, global convergence of the stochastic gradient bandit algorithm has not been previously established, even though it is an old algorithm known to be applicable to bandits. The new result is achieved by establishing two novel technical findings: first, the noise of the stochastic updates in the gradient bandit algorithm satisfies a strong “growth condition” property, where the variance diminishes whenever progress becomes small, implying that additional noise control via diminishing step sizes is unnecessary; second, a form of “weak exploration” is automatically achieved through the stochastic gradient updates, since they prevent the action probabilities from decaying faster than O(1/t), thus ensuring that every action is sampled infinitely often with probability 1. These two findings can be used to show that the stochastic gradient update is already “sufficient” for bandits in the sense that exploration versus exploitation is automatically balanced in a manner that ensures almost sure convergence to a global optimum. These novel theoretical findings are further verified by experimental results.

A Fast, Well-Founded Approximation to the Empirical Neural Tangent Kernel

Mohamad Amin Mohamadi, Wonho Bae, Danica J. Sutherland

Abstract: Empirical neural tangent kernels (eNTKs) can provide a good understanding of a given network's representation: they are often far less expensive to compute and applicable more broadly than infinite width NTKs. For networks with O output units (e.g. an O-class classifier), however, the eNTK on N inputs is of size NO×NO, taking O((NO)2) memory and up to O((NO)3) computation. Most existing applications have therefore used one of a handful of approximations yielding N×N kernel matrices, saving orders of magnitude of computation, but with limited to no justification. We prove that one such approximation, which we call "sum of logits", converges to the true eNTK at initialization for any network with a wide final "readout" layer. Our experiments demonstrate the quality of this approximation for various uses across a range of settings.

Trajectory-Aware Eligibility Traces for Off-Policy Reinforcement Learning

Brett Daley, Martha White, Christopher Amato, Marlos C. Machado

Abstract: Off-policy learning from multistep returns is crucial for sample-efficient reinforcement learning, but counteracting off-policy bias without exacerbating variance is challenging. Classically, off-policy bias is corrected in a per-decision manner: past temporal-difference errors are re-weighted by the instantaneous Importance Sampling (IS) ratio after each action via eligibility traces. Many off-policy algorithms rely on this mechanism, along with differing protocols for cutting the IS ratios to combat the variance of the IS estimator. Unfortunately, once a trace has been fully cut, the effect cannot be reversed. This has led to the development of credit-assignment strategies that account for multiple past experiences at a time. These trajectory-aware methods have not been extensively analyzed, and their theoretical justification remains uncertain. In this paper, we propose a multistep operator that can express both per-decision and trajectory-aware methods. We prove convergence conditions for our operator in the tabular setting, establishing the first guarantees for several existing methods as well as many new ones. Finally, we introduce Recency-Bounded Importance Sampling (RBIS), which leverages trajectory awareness to perform robustly across λ-values in an off-policy control task.

Exphormer: Sparse Transformers for Graphs

Hamed Shirzad, Ameya Velingker, Balaji Venkatachalam, Danica J. Sutherland, Ali Kemal Sinop

Abstract: Graph transformers have emerged as a promising architecture for a variety of graph learning and representation tasks. Despite their successes, though, it remains challenging to scale graph transformers to large graphs while maintaining accuracy competitive with message-passing networks. In this paper, we introduce Exphormer, a framework for building powerful and scalable graph transformers. Exphormer consists of a sparse attention mechanism based on two mechanisms: virtual global nodes and expander graphs, whose mathematical characteristics, such as spectral expansion, pseduorandomness, and sparsity, yield graph transformers with complexity only linear in the size of the graph, while allowing us to prove desirable theoretical properties of the resulting transformer models. We show that incorporating Exphormer into the recently-proposed GraphGPS framework produces models with competitive empirical results on a wide variety of graph datasets, including state-of-the-art results on three datasets. We also show that Exphormer can scale to datasets on larger graphs than shown in previous graph transformer architectures.

The Optimal Approximation Factors in Misspecified Off-Policy Value Function Estimation

Philip Amortila, Nan Jiang, Csaba Szepesvari

Abstract: Theoretical guarantees in reinforcement learning (RL) are known to suffer multiplicative blow-up factors with respect to the misspecification error of function approximation. Yet, the nature of such approximation factors---especially their optimal form in a given learning problem---is poorly understood. In this paper we study this question in linear off-policy value function estimation, where many open questions remain. We study the approximation factor in a broad spectrum of settings, such as presence vs. absence of state aliasing and full vs. partial coverage of the state space. Our core results include instance-dependent upper bounds on the approximation factors with respect to both the weighted L(2)-norm (where the weighting is the offline state distribution) and the L(∞) norm. We show that these approximation factors are optimal (in an instance-dependent sense) for a number of these settings. In other cases, we show that the instance-dependent parameters which appear in the upper bounds are necessary, and that the finiteness of either alone cannot guarantee a finite approximation factor even in the limit of infinite data.

Revisiting Simple Regret: Fast Rates for Returning a Good Arm

Yao Zhao, Connor James Stephens, Csaba Szepesvári, Kwang-Sung Jun

Abstract: Simple regret is a natural and parameter-free performance criterion for pure exploration in multi-armed bandits yet is less popular than the probability of missing the best arm or an ϵ-good arm, perhaps due to lack of easy ways to characterize it. In this paper, we make significant progress on minimizing simple regret in both data-rich (T≥n) and data-poor regime (T≤n) where n is the number of arms, and T is the number of samples. At its heart is our improved instance-dependent analysis of the well-known Sequential Halving (SH) algorithm, where we bound the probability of returning an arm whose mean reward is not within ϵ from the best (i.e., not ϵ-good) for \textit{any} choice of ϵ>0, although ϵ is not an input to SH. Our bound not only leads to an optimal worst-case simple regret bound of n/T‾‾‾‾√ up to logarithmic factors but also essentially matches the instance-dependent lower bound for returning an ϵ-good arm reported by Katz-Samuels and Jamieson (2020). For the more challenging data-poor regime, we propose Bracketing SH (BSH) that enjoys the same improvement even without sampling each arm at least once. Our empirical study shows that BSH outperforms existing methods on real-world tasks.

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