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Probabilistic Methods · Bayesian Models and Methods

Mohammad Al-Jarrah, Niyizhen Jin, Bamdad Hosseini, Amirhossein Taghvaei

This paper is concerned with the problem of nonlinear filtering, i.e., computing the conditional distribution of the state of a stochastic dynamical system given a history of noisy partial observations. Conventional sequential importance resampling (SIR) particle filters suffer from fundamental limitations, in scenarios involving degenerate likelihoods or high-dimensional states, due to the weight degeneracy issue. In this paper, we explore an alternative method, which is based on estimating the Brenier optimal transport (OT) map from the current prior distribution of the state to the posterior distribution at the next time step. Unlike SIR particle filters, the OT formulation does not require the analytical form of the likelihood. Moreover, it allows us to harness the approximation power of neural networks to model complex and multi-modal distributions and employ stochastic optimization algorithms to enhance scalability. Extensive numerical experiments are presented that compare the OT method to the SIR particle filter and the ensemble Kalman filter, evaluating the performance in terms of sample efficiency, high-dimensional scalability, and the ability to capture complex and multi-modal distributions.

Xun Deng, Junlong Liu, Han Zhong, Fuli Feng, Chen Shen, Xiangnan He, Jieping Ye, Zheng Wang

Active clustering aims to boost the clustering performance by integrating human-annotated pairwise constraints through strategic querying. Conventional approaches with semi-supervised clustering schemes encounter high query costs when applied to large datasets with numerous classes. To address these limitations, we propose a novel Adaptive Active Aggregation and Splitting (A3S) framework, falling within the cluster-adjustment scheme in active clustering. A3S features strategic active clustering adjustment on the initial cluster result, which is obtained by an adaptive clustering algorithm. In particular, our cluster adjustment is inspired by the quantitative analysis of Normalized mutual information gain under the information theory framework and can provably improve the clustering quality. The proposed A3S framework significantly elevates the performance and scalability of active clustering. In extensive experiments across diverse real-world datasets, A3S achieves desired results with significantly fewer human queries compared with existing methods.

Reinforcement Learning

Yingru Li, Jiawei Xu, Lei Han, Zhi-Quan Luo

We propose HyperAgent, a reinforcement learning (RL) algorithm based on the hypermodel framework for exploration in RL. HyperAgent allows for the efficient incremental approximation of posteriors associated with an optimal action-value function ($Q^\star$) without the need for conjugacy and follows the greedy policies w.r.t. these approximate posterior samples. We demonstrate that HyperAgent offers robust performance in large-scale deep RL benchmarks. It can solve Deep Sea hard exploration problems with episodes that optimally scale with problem size and exhibits significant efficiency gains in the Atari suite. Implementing HyperAgent requires minimal code addition to well-established deep RL frameworks like DQN. We theoretically prove that, under tabular assumptions, HyperAgent achieves logarithmic per-step computational complexity while attaining sublinear regret, matching the best known randomized tabular RL algorithm.

Miscellaneous Aspects of Machine Learning · Causality

Joshua Loftus

Causal models and methods have great promise, but their progress has been stalled. Proposals using causality get squeezed between two opposing worldviews. Scientific perfectionism--an insistence on only using ``correct'' models--slows the adoption of causal methods in knowledge generating applications. Pushing in the opposite direction, the academic discipline of computer science prefers algorithms with no or few assumptions, and technologies based on automation and scalability are often selected for economic and business applications. We argue that these system-centric inductive biases should be replaced with a human-centric philosophy we refer to as scientific pragmatism. The machine learning community must strike the right balance to make space for the causal revolution to prosper.

Optimization · Discrete and Combinatorial Optimization

Vicente Balmaseda, Ying Xu, Yixin Cao, Nate Veldt

Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a tighter analysis of two previous approximation algorithms, improving their approximation guarantees from 4 to 3. Moreover, we show that both algorithms can be derandomized in a surprisingly simple way, by greedily taking a vertex of maximum degree in an auxiliary graph and forming a cluster around it. One of these algorithms relies on solving a linear program. Our final contribution is to design a new and purely combinatorial approach for doing so that is far more scalable in theory and practice.

Miscellaneous Aspects of Machine Learning · Scalable Algorithms

Samir Khaki, Konstantinos Plataniotis

We introduce the $\textbf{O}$ne-shot $\textbf{P}$runing $\textbf{T}$echnique for $\textbf{I}$nterchangeable $\textbf{N}$etworks ($\textbf{OPTIN}$) framework as a tool to increase the efficiency of pre-trained transformer architectures $\textit{without requiring re-training}$. Recent works have explored improving transformer efficiency, however often incur computationally expensive re-training procedures or depend on architecture-specific characteristics, thus impeding practical wide-scale adoption. To address these shortcomings, the OPTIN framework leverages intermediate feature distillation, capturing the long-range dependencies of model parameters (coined $\textit{trajectory}$), to produce state-of-the-art results on natural language, image classification, transfer learning, and semantic segmentation tasks $\textit{without re-training}$. Given a FLOP constraint, the OPTIN framework will compress the network while maintaining competitive accuracy performance and improved throughput. Particularly, we show a $\leq 2$% accuracy degradation from NLP baselines and a $0.5$% improvement from state-of-the-art methods on image classification at competitive FLOPs reductions. We further demonstrate the generalization of tasks and architecture with comparative performance using Mask2Former for semantic segmentation and cnn-style networks. OPTIN presents one of the first one-shot efficient frameworks for compressing transformer architectures that generalizes well across different class domains, in particular: natural language and image-related tasks, without $\textit{re-training}$.

Yubo Zhuang, Xiaohui Chen, Yun Yang, Richard Zhang

$K$-means clustering is a widely used machine learning method for identifying patterns in large datasets. Recently, semidefinite programming (SDP) relaxations have been proposed for solving the $K$-means optimization problem, which enjoy strong statistical optimality guarantees. However, the prohibitive cost of implementing an SDP solver renders these guarantees inaccessible to practical datasets. In contrast, nonnegative matrix factorization (NMF) is a simple clustering algorithm widely used by machine learning practitioners, but it lacks a solid statistical underpinning and theoretical guarantees. In this paper, we consider an NMF-like algorithm that solves a nonnegative low-rank restriction of the SDP-relaxed $K$-means formulation using a nonconvex Burer--Monteiro factorization approach. The resulting algorithm is as simple and scalable as state-of-the-art NMF algorithms while also enjoying the same strong statistical optimality guarantees as the SDP. In our experiments, we observe that our algorithm achieves significantly smaller mis-clustering errors compared to the existing state-of-the-art while maintaining scalability.

Probabilistic Methods · Monte Carlo and Sampling Methods

Isaac Reid, Krzysztof Choromanski, Eli Berger, Adrian Weller

We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined general graph random features (g-GRFs). This includes many of the most popular examples of kernels defined on the nodes of a graph. Our algorithm enjoys subquadratic time complexity with respect to the number of nodes, overcoming the notoriously prohibitive cubic scaling of exact graph kernel evaluation. It can also be trivially distributed across machines, permitting learning on much larger networks. At the heart of the algorithm is a modulation function which upweights or downweights the contribution from different random walks depending on their lengths. We show that by parameterising it with a neural network we can obtain g-GRFs that give higher-quality kernel estimates or perform efficient, scalable kernel learning. We provide robust theoretical analysis and support our findings with experiments including pointwise estimation of fixed graph kernels, solving non-homogeneous graph ordinary differential equations, node clustering and kernel regression on triangular meshes.

Hong Liu, Zhiyuan Li, David Hall, Percy Liang, Tengyu Ma

Given the massive cost of language model pre-training, a non-trivial improvement of the optimization algorithm would lead to a material reduction on the time and cost of training. Adam and its variants have been state-of-the-art for years, and more sophisticated second-order (Hessian-based) optimizers often incur too much per-step overhead. In this paper, we propose Sophia, a simple scalable second-order optimizer that uses a light-weight estimate of the diagonal Hessian as the pre-conditioner. The update is the moving average of the gradients divided by the moving average of the estimated Hessian, followed by element-wise clipping. The clipping controls the worst-case update size and tames the negative impact of non-convexity and rapid change of Hessian along the trajectory. Sophia only estimates the diagonal Hessian every handful of iterations, which has negligible average per-step time and memory overhead. On language modeling with GPT models of sizes ranging from 125M to 1.5B, Sophia achieves a 2x speed-up compared to Adam in the number of steps, total compute, and wall-clock time, achieving the same perplexity with 50\% fewer steps, less total compute, and reduced wall-clock time.

Reinforcement Learning

Mahdi Kallel, Debabrota Basu, Riad Akrour, Carlo D'Eramo

Deterministic policies are often preferred over stochastic ones when implemented on physical systems. They can prevent erratic and harmful behaviors while being easier to implement and interpret. However, in practice, exploration is largely performed by stochastic policies.First-order Bayesian Optimization (BO) methods offer a principled way of performing exploration using deterministic policies. This is done through a learned probabilistic model of the objective function and its gradient. Nonetheless, such approaches treat policy search as a black-box problem, and thus, neglect the reinforcement learning nature of the problem. In this work, we leverage the performance difference lemma to introduce a novel mean function for the probabilistic model. This results in augmenting BO methods with the action-value function. Hence, we call our method Augmented Bayesian Search (ABS).Interestingly, this new mean function enhances the posterior gradient with the deterministic policy gradient, effectively bridging the gap between BO and policy gradient methods. The resulting algorithm combines the convenience of the direct policy search with the scalability of reinforcement learning.We validate ABS on high-dimensional locomotion problems and demonstrate competitive performance compared to existing direct policy search schemes.

Khurram Javed, Haseeb Shah, Richard Sutton, Martha White

Constructing states from sequences of observations is an important component of reinforcement learning agents. One solution for state construction is to use recurrent neural networks. Back-propagation through time (BPTT), and real-time recurrent learning (RTRL) are two popular gradient-based methods for recurrent learning. BPTT requires complete trajectories of observations before it can compute the gradients and is unsuitable for online updates. RTRL can do online updates but scales poorly to large networks. In this paper, we propose two constraints that make RTRL scalable. We show that by either decomposing the network into independent modules or learning the network in stages, we can make RTRL scale linearly with the number of parameters. Unlike prior scalable gradient estimation algorithms, such as UORO and Truncated-BPTT, our algorithms do not add noise or bias to the gradient estimate. Instead, they trade off the functional capacity of the network for computationally efficient learning. We demonstrate the effectiveness of our approach over Truncated-BPTT on a prediction benchmark inspired by animal learning and by doing policy evaluation of pre-trained policies for Atari 2600 games.

Miscellaneous Aspects of Machine Learning · Representation Learning

Philippe Chlenski, Ethan Turok, Antonio Moretti, Itsik Pe'er

Hyperbolic geometry is gaining traction in machine learning due to its capacity to effectively capture hierarchical structures in real-world data. Hyperbolic spaces, where neighborhoods grow exponentially, offer substantial advantages and have consistently delivered state-of-the-art results across diverse applications. However, hyperbolic classifiers often grapple with computational challenges. Methods reliant on Riemannian optimization frequently exhibit sluggishness, stemming from the increased computational demands of operations on Riemannian manifolds. In response to these challenges, we present HyperDT, a novel extension of decision tree algorithms into hyperbolic space. Crucially, HyperDT eliminates the need for computationally intensive Riemannian optimization, numerically unstable exponential and logarithmic maps, or pairwise comparisons between points by leveraging inner products to adapt Euclidean decision tree algorithms to hyperbolic space. Our approach is conceptually straightforward and maintains constant-time decision complexity while mitigating the scalability issues inherent in high-dimensional Euclidean spaces. Building upon HyperDT, we introduce HyperRF, a hyperbolic random forest model. Extensive benchmarking across diverse datasets underscores the superior performance of these models, providing a swift, precise, accurate, and user-friendly toolkit for hyperbolic data analysis.

Reinforcement Learning · Multi-agent

Kai Cui, Sascha Hauck, Christian Fabian, Heinz Koeppl

Recent reinforcement learning (RL) methods have achieved success in various domains. However, multi-agent RL (MARL) remains a challenge in terms of decentralization, partial observability and scalability to many agents. Meanwhile, collective behavior requires resolution of the aforementioned challenges, and remains of importance to many state-of-the-art applications such as active matter physics, self-organizing systems, opinion dynamics, and biological or robotic swarms. Here, MARL via mean field control (MFC) offers a potential solution to scalability, but fails to consider decentralized and partially observable systems. In this paper, we enable decentralized behavior of agents under partial information by proposing novel models for decentralized partially observable MFC (Dec-POMFC), a broad class of problems with permutation-invariant agents allowing for reduction to tractable single-agent Markov decision processes (MDP) with single-agent RL solution. We provide rigorous theoretical results, including a dynamic programming principle, together with optimality guarantees for Dec-POMFC solutions applied to finite swarms of interest. Algorithmically, we propose Dec-POMFC-based policy gradient methods for MARL via centralized training and decentralized execution, together with policy gradient approximation guarantees. In addition, we improve upon state-of-the-art histogram-based MFC by kernel methods, which is of separate interest also for fully observable MFC. We evaluate numerically on representative collective behavior tasks such as adapted Kuramoto and Vicsek swarming models, being on par with state-of-the-art MARL. Overall, our framework takes a step towards RL-based engineering of artificial collective behavior via MFC.

Optimization · Zero-order and Black-box Optimization

Scott Sussex, Pier Giuseppe Sessa, Anastasia Makarova, Andreas Krause

In Causal Bayesian Optimization (CBO), an agent intervenes on a structural causal model with known graph but unknown mechanisms to maximize a downstream reward variable. In this paper, we consider the generalization where other agents or external events also intervene on the system, which is key for enabling adaptiveness to non-stationarities such as weather changes, market forces, or adversaries. We formalize this generalization of CBO as Adversarial Causal Bayesian Optimization (ACBO) and introduce the first algorithm for ACBO with bounded regret: Causal Bayesian Optimization with Multiplicative Weights (CBO-MW). Our approach combines a classical online learning strategy with causal modeling of the rewards. To achieve this, it computes optimistic counterfactual reward estimates by propagating uncertainty through the causal graph. We derive regret bounds for CBO-MW that naturally depend on graph-related quantities. We further propose a scalable implementation for the case of combinatorial interventions and submodular rewards. Empirically, CBO-MW outperforms non-causal and non-adversarial Bayesian optimization methods on synthetic environments and environments based on real-word data. Our experiments include a realistic demonstration of how CBO-MW can be used to learn users' demand patterns in a shared mobility system and reposition vehicles in strategic areas.

Shikai Fang, Xin Yu, Zheng Wang, Shibo Li, Mike Kirby, Shandian Zhe

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there are finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, real-world data is often not naturally posed in this setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions. Then, we convert each GP into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications. We release the code of FunBaT at {https://github.com/xuangu-fang/Functional-Bayesian-Tucker-Decomposition}.

Deep Learning · Robustness

Hyunho Kim, Jong-Seok Lee

In this research, we focus on the problem of learning monotonic neural networks, as preserving the monotonicity of a model with respect to a subset of inputs is crucial for practical applications across various domains. Although several methods have recently been proposed to address this problem, they have limitations such as not guaranteeing monotonicity in certain cases, requiring additional inference time, lacking scalability with increasing network size and number of monotonic inputs, and manipulating network weights during training. To overcome these limitations, we introduce a simple but novel architecture of the partially connected network which incorporates a 'scalable monotonic hidden layer' comprising three units: the exponentiated unit, ReLU unit, and confluence unit. This allows for the repetitive integration of the scalable monotonic hidden layers without other structural constraints. Consequently, our method offers ease of implementation and rapid training through the conventional error-backpropagation algorithm. We accordingly term this method as Scalable Monotonic Neural Networks (SMNN). Numerical experiments demonstrated that our method achieved comparable prediction accuracy to the state-of-the-art approaches while effectively addressing the aforementioned weaknesses.

Reinforcement Learning

Zhiyu Mei, Wei Fu, Jiaxuan Gao, Guangju Wang, Huanchen Zhang, Yi Wu

The ever-growing complexity of reinforcement learning (RL) tasks demands a distributed system to efficiently generate and process a massive amount of data. However, existing open-source libraries suffer from various limitations, which impede their practical use in challenging scenarios where large-scale training is necessary. In this paper, we present a novel abstraction on the dataflows of RLtraining, which unifies diverse RL training applications into a general framework. Following this abstraction, we develop a scalable, efficient, and extensible distributed RL system called ReaLly Scalable RL (SRL), which allows efficient and massively parallelized training and easy development of customized algorithms. Our evaluation shows that SRL outperforms existing academic libraries, reaching at most 21x higher training throughput in a distributed setting. On learning performance, beyond performing and scaling well on common RL benchmarks with different RL algorithms, SRL can reproduce the same solution in the challenging hide-and-seek environment as reported by OpenAI with up to 5x speedup in wallclock time. Notably, SRL is the first in the academic community to perform RL experiments at a large scale with over 15k CPU cores. SRL anonymous repository is available at: https://anonymous.4open.science/r/srl-1E45/.

Deep Learning · Large Language Models

Pingzhi Li, Zhenyu Zhang, Prateek Yadav, Yi-Lin Sung, Yu Cheng, Mohit Bansal, Tianlong Chen

Sparsely activated Mixture-of-Experts (SMoE) has shown promise to scale up the learning capacity of neural networks, however, they have issues like: ($a$) $\textit{High Memory Usage,}$ due to duplication of the network layers into multiple copies as experts; and ($b$) $\textit{Redundancy in Experts,}$ as common learning-based routing policies suffer from representational collapse. Therefore, vanilla SMoE models are memory inefficient and non-scalable, especially for resource-constrained downstream scenarios. In this paper, we ask: Can we craft a compact SMoE model by consolidating expert information? What is the best recipe to merge multiple experts into fewer but more knowledgeable experts? Our pilot investigation reveals that conventional model merging methods fail to be effective in such expert merging for SMoE. The potential reasons are: ($1$) redundant information overshadows critical experts; ($2$) appropriate neuron permutation for each expert is missing to bring all of them in alignment. To address these challenges, we propose a novel merging algorithm for SMoE, $\textit{i.e.}$, $\texttt{M-SMoE}$, which leverages routing statistics to guide expert merging. Specifically, it starts with neuron permutation alignment for experts; then, dominant experts and their "group members" are formed based on routing policies; lastly, every expert group is merged into a single expert by utilizing each expert's activation frequency as their weight for merging, thus diminishing the impact of insignificant experts. Moreover, we draw an interesting observation that our proposed merging promotes a low dimensionality in the merged expert's weight space, naturally paving the way for additional compression. Hence, our final method, $\texttt{MC-SMoE}$ ($\textit{i.e.}$, Merge, then Compress SMoE), further decomposes the merged experts into low-rank and structural sparse alternatives. Extensive experiments across $8$ benchmarks validate the effectiveness of our proposals. For instance, our $\texttt{MC-SMoE}$ achieves up to $80\%$ memory and a $20\%$ FLOPs reduction, with virtually no loss in performance. Our code is provided as supplementary material.

Reinforcement Learning · Deep RL

Frank Shih, Faming Liang

Reinforcement learning (RL) tackles sequential decision-making problems by creatingagents that interacts with their environment. However, existing algorithms often view these problem as static, focusing on point estimates for model parameters to maximize expected rewards, neglecting the stochastic dynamics of agent-environment interactions and the critical role of uncertainty quantification.Our research leverages the Kalman filtering paradigm to introduce a novel and scalable sampling algorithm called Langevinized Kalman Temporal-Difference (LKTD) for deep reinforcement learning. This algorithm, grounded in Stochastic Gradient Markov Chain Monte Carlo (SGMCMC), efficiently draws samples from the posterior distribution of deep neural network parameters. Under mild conditions, we prove that the posterior samples generated by the LKTD algorithm converge to a stationary distribution. This convergence not only enables us to quantify uncertainties associated with the value function and model parameters but also allows us to monitor these uncertainties during policy updates throughout the training phase. The LKTD algorithm paves the way for more robust and adaptable reinforcement learning approaches.

Reinforcement Learning

Mehdi Zadem, Sergio Mover, Sao Mai Nguyen

Goal representation affects the performance of Hierarchical Reinforcement Learn- ing (HRL) algorithms by decomposing the complex learning problem into easier subtasks. Recent studies show that representations that preserve temporally ab- stract environment dynamics are successful in solving difficult problems and pro- vide theoretical guarantees for optimality. These methods however cannot scale to tasks where environment dynamics increase in complexity i.e. the temporally abstract transition relations depend on larger number of variables. On the other hand, other efforts have tried to use spatial abstraction to mitigate the previous issues. Their limitations include scalability to high dimensional environments and dependency on prior knowledge.In this paper, we propose a novel three-layer HRL algorithm that introduces, at different levels of the hierarchy, both a spatial and a temporal goal abstraction. We provide a theoretical study of the regret bounds of the learned policies. We evaluate the approach on complex continuous control tasks, demonstrating the effectiveness of spatial and temporal abstractions learned by this approach.