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Social Aspects/Accountability, Transparency and Interpretability

Kyosuke Morita

Scope of ReproducibilityThis study aims to reproduce the results of the paper 'FOCUS: Flexible Optimizable Counterfactual Explanations for Tree Ensembles' by Lucic et al.The main claims of the original paper are that FOCUS is able to (i) generate counterfactual explanations for all the instances in a dataset; and (ii) find counterfactual explanations that are closer to the original input for tree-based algorithms than existing methods.MethodologyThis study replicates the original experiments using the code, data, and models provided by the authors. Additionally, this study re-implements code and retrains the models to evaluate the robustness and generality of FOCUS.All the experiments were conducted on a personal laptop with a quad-core CPU with 8GB of RAM and it approximately took 33 hours in total.ResultsThis study was able to replicate the results of the original paper in terms of finding counterfactual explanations for all instances in datasets. Additional experiments were conducted to validate the robustness and generality of the conclusion. While there were slight deviations in terms of generating smaller mean distances, half of the models still outperformed the results of the existing method.What was easyThe implementation of the original paper is publicly available on GitHub. The repository contains the models and data used in the original experiments. Also, the authors provided a technical appendix, which includes all the hyperparameters that were used for the experiments for reproduction upon request.What was difficultAlthough the implementation code was available, it employs outdated packages and the code structure is complex. Also, the comments in the functions and the documentation of the code are sparse or nonexistent, which made it difficult to follow the code.Communication with original authorsI reached out to the authors to obtain the hyperparameters used in the experiments. The authors responded promptly with a detailed technical appendix of the original paper.

Theory/Reinforcement Learning and Planning

Hanlin Zhu, Amy Zhang

Goal-conditioned reinforcement learning (GCRL) refers to learning general-purpose skills that aim to reach diverse goals. In particular, offline GCRL only requires purely pre-collected datasets to perform training tasks without additional interactions with the environment. Although offline GCRL has become increasingly prevalent and many previous works have demonstrated its empirical success, the theoretical understanding of efficient offline GCRL algorithms is not well established, especially when the state space is huge and the offline dataset only covers the policy we aim to learn. In this paper, we provide a rigorous theoretical analysis of an existing empirically successful offline GCRL algorithm. We prove that under slight modification, this algorithm enjoys an $\tilde{O}(\text{poly}(1/\epsilon))$ sample complexity (where $\epsilon$ is the desired suboptimality of the learned policy) with general function approximation thanks to the property of (semi-)strong convexity of the objective functions. We only require nearly minimal assumptions on the dataset (single-policy concentrability) and the function class (realizability). Moreover, this algorithm consists of two uninterleaved optimization steps, which we refer to as $V$-learning and policy learning, and is computationally stable since it does not involve minimax optimization. We also empirically validate our theory by showing that the modified algorithm outperforms the previous algorithm in various real-world environments.To the best of our knowledge, this is the first algorithm that is both provably efficient with general function approximation and single-policy concentrability, and empirically successful without requiring solving minimax optimization problems.

Theory/Reinforcement Learning and Planning

Shangtong Zhang, Remi Tachet des Combes, Romain Laroche

In this paper, we establish the global optimality and convergence rate of an off-policy actor critic algorithm in the tabular setting without using density ratio to correct the discrepancy between the state distribution of the behavior policy and that of the target policy. Our work goes beyond existing works on the optimality of policy gradient methods in that existing works use the exact policy gradient for updating the policy parameters while we use an approximate and stochastic update step. Our update step is not a gradient update because we do not use a density ratio to correct the state distribution, which aligns well with what practitioners do. Our update is approximate because we use a learned critic instead of the true value function. Our update is stochastic because at each step the update is done for only the current state action pair. Moreover, we remove several restrictive assumptions from existing works in our analysis. Central to our work is the finite sample analysis of a generic stochastic approximation algorithm with time-inhomogeneous update operators on time-inhomogeneous Markov chains, based on its uniform contraction properties.

Optimization/Control and Optimization

Wenqi Cui, Yan Jiang, Baosen Zhang, Yuanyuan Shi

We study the optimal control of multiple-input and multiple-output dynamical systems via the design of neural network-based controllers with stability and output tracking guarantees. While neural network-based nonlinear controllers have shown superior performance in various applications, their lack of provable guarantees has restricted their adoption in high-stake real-world applications. This paper bridges the gap between neural network-based controllers and the need for stabilization guarantees. Using equilibrium-independent passivity, a property present in a wide range of physical systems, we propose neural Proportional-Integral (PI) controllers that have provable guarantees of stability and zero steady-state output tracking error. The key structure is the strict monotonicity on proportional and integral terms, which is parameterized as gradients of strictly convex neural networks (SCNN). We construct SCNN with tunable softplus-$\beta$ activations, which yields universal approximation capability and is also useful in incorporating communication constraints. In addition, the SCNNs serve as Lyapunov functions, giving us end-to-end performance guarantees. Experiments on traffic and power networks demonstrate that the proposed approach improves both transient and steady-state performances, while unstructured neural networks lead to unstable behaviors.

Probabilistic Methods/Bayesian Models and Methods

Fabian Zaiser, Andrzej Murawski, Chih-Hao Luke Ong

We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors.To express such models, we introduce a probabilistic programming language that supports discrete and continuous sampling, discrete observations, affine functions, (stochastic) branching, and conditioning on discrete events.Our key tool is *probability generating functions*:they provide a compact closed-form representation of distributions that are definable by programs, thus enabling the exact computation of posterior probabilities, expectation, variance, and higher moments.Our inference method is provably correct and fully automated in a tool called *Genfer*, which uses automatic differentiation (specifically, Taylor polynomials), but does not require computer algebra.Our experiments show that Genfer is often faster than the existing exact inference tools PSI, Dice, and Prodigy.On a range of real-world inference problems that none of these exact tools can solve, Genfer's performance is competitive with approximate Monte Carlo methods, while avoiding approximation errors.

Deep Learning/Algorithms

Yihan Wang, Jatin Chauhan, Wei Wang, Cho-Jui Hsieh

Despite the demonstrated empirical efficacy of prompt tuning to adapt a pretrained language model for a new task, the theoretical underpinnings of the difference between "tuning parameters before the input" against "the tuning of model weights" are limited. We thus take one of the first steps to understand the role of soft-prompt tuning for transformer-based architectures. By considering a general purpose architecture, we analyze prompt tuning from the lens of both: universal approximation and limitations with finite-depth fixed-weight pretrained transformers for continuous-valued functions. Our universality result guarantees the existence of a strong transformer with a prompt to approximate any sequence-to-sequence function in the set of Lipschitz functions. The limitations of prompt tuning for limited-depth transformers are first proved by constructing a set of datasets, that cannot be memorized by a prompt of any length for a given single encoder layer. We also provide a lower bound on the required number of tunable prompt parameters and compare the result with the number of parameters required for a low-rank update (based on LoRA) for a single-layer setting. We finally extend our analysis to multi-layer settings by providing sufficient conditions under which the transformer can at best learn datasets from invertible functions only. Our theoretical claims are also corroborated by empirical results.

Jincheng Mei, Bo Dai, Alekh Agarwal, Mohammad Ghavamzadeh, Csaba Szepesvari, Dale Schuurmans

We prove that, for finite-arm bandits with linear function approximation, the global convergence of policy gradient (PG) methods depends on inter-related properties between the policy update and the representation. textcolor{blue}{First}, we establish a few key observations that frame the study: \textbf{(i)} Global convergence can be achieved under linear function approximation without policy or reward realizability, both for the standard Softmax PG and natural policy gradient (NPG). \textbf{(ii)} Approximation error is not a key quantity for characterizing global convergence in either algorithm. \textbf{(iii)} The conditions on the representation that imply global convergence are different between these two algorithms. Overall, these observations call into question approximation error as an appropriate quantity for characterizing the global convergence of PG methods under linear function approximation. \textcolor{blue}{Second}, motivated by these observations, we establish new general results: \textbf{(i)} NPG with linear function approximation achieves global convergence \emph{if and only if} the projection of the reward onto the representable space preserves the optimal action's rank, a quantity that is not strongly related to approximation error. \textbf{(ii)} The global convergence of Softmax PG occurs if the representation satisfies a non-domination condition and can preserve the ranking of rewards, which goes well beyond policy or reward realizability. We provide experimental results to support these theoretical findings.

Mina Dalirrooyfard, Slobodan Mitrovic, Yuriy Nevmyvaka

Finding min $s$-$t$ cuts in graphs is a basic algorithmic tool, with applications in image segmentation, community detection, reinforcement learning, and data clustering. In this problem, we are given two nodes as terminals and the goal is to remove the smallest number of edges from the graph so that these two terminals are disconnected. We study the complexity of differential privacy for the min $s$-$t$ cut problem and show nearly tight lower and upper bounds where we achieve privacy at no cost for running time efficiency. We also develop a differentially private algorithm for the multiway $k$-cut problem, in which we are given $k$ nodes as terminals that we would like to disconnect. As a function of $k$, we obtain privacy guarantees that are exponentially more efficient than applying the advanced composition theorem to known algorithms for multiway $k$-cut. Finally, we empirically evaluate the approximation of our differentially private min $s$-$t$ cut algorithm and show that it almost matches the quality of the output of non-private ones.

Theory/Reinforcement Learning and Planning

Gellert Weisz, András György, Csaba Szepesvari

We consider online reinforcement learning (RL) in episodic Markov decision processes (MDPs) under the linear $q^\pi$-realizability assumption, where it is assumed that the action-values of all policies can be expressed as linear functions of state-action features. This class is known to be more general than linear MDPs, where the transition kernel and the reward function are assumed to be linear functions of the feature vectors. As our first contribution, we show that the difference between the two classes is the presence of states in linearly $q^\pi$-realizable MDPs where for any policy, all the actions have approximately equal values, and skipping over these states by following an arbitrarily fixed policy in those states transforms the problem to a linear MDP. Based on this observation, we derive a novel (computationally inefficient) learning algorithm for linearly $q^\pi$-realizable MDPs that simultaneously learns what states should be skipped over and runs another learning algorithm on the linear MDP hidden in the problem. The method returns an $\epsilon$-optimal policy after $\text{polylog}(H, d)/\epsilon^2$ interactions with the MDP, where $H$ is the time horizon and $d$ is the dimension of the feature vectors, giving the first polynomial-sample-complexity online RL algorithm for this setting. The results are proved for the misspecified case, where the sample complexity is shown to degrade gracefully with the misspecification error.

Fabian Zaiser, Andrzej Murawski, Chih-Hao Luke Ong

We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors.To express such models, we introduce a probabilistic programming language that supports discrete and continuous sampling, discrete observations, affine functions, (stochastic) branching, and conditioning on discrete events.Our key tool is *probability generating functions*:they provide a compact closed-form representation of distributions that are definable by programs, thus enabling the exact computation of posterior probabilities, expectation, variance, and higher moments.Our inference method is provably correct and fully automated in a tool called *Genfer*, which uses automatic differentiation (specifically, Taylor polynomials), but does not require computer algebra.Our experiments show that Genfer is often faster than the existing exact inference tools PSI, Dice, and Prodigy.On a range of real-world inference problems that none of these exact tools can solve, Genfer's performance is competitive with approximate Monte Carlo methods, while avoiding approximation errors.

Miscellaneous Aspects of Machine Learning/Online Learning, Active Learning and Bandits

Haoting Zhang, Jinghai He, Rhonda Righter, Zuo-Jun Shen, Zeyu Zheng

Contextual decision-making problems have witnessed extensive applications in various fields such as online content recommendation, personalized healthcare, and autonomous vehicles, where a core practical challenge is to select a suitable surrogate model for capturing unknown complicated reward functions. It is often the case that both high approximation accuracy and explicit uncertainty quantification are desired. In this work, we propose a neural network-accompanied Gaussian process (NN-AGP) model, which leverages neural networks to approximate the unknown and potentially complicated reward function regarding the contextual variable, and maintains a Gaussian process surrogate model with respect to the decision variable. Our model is shown to outperform existing approaches by offering better approximation accuracy thanks to the use of neural networks and possessing explicit uncertainty quantification from the Gaussian process. We also analyze the maximum information gain of the NN-AGP model and prove regret bounds for the corresponding algorithms. Moreover, we conduct experiments on both synthetic and practical problems, illustrating the effectiveness of our approach.

Aldo Pacchiano, Jonathan Lee, Emma Brunskill

We study the problem of experiment planning with function approximation in contextual bandit problems. In settings where there is a significant overhead to deploying adaptive algorithms---for example, when the execution of the data collection policies is required to be distributed, or a human in the loop is needed to implement these policies---producing in advance a set of policies for data collection is paramount. We study the setting where a large dataset of contexts but not rewards is available and may be used by the learner to design an effective data collection strategy. Although when rewards are linear this problem has been well studied, results are still missing for more complex reward models. In this work we propose two experiment planning strategies compatible with function approximation. The first is an eluder planning and sampling procedure that can recover optimality guarantees depending on the eluder dimension of the reward function class. For the second, we show that a uniform sampler achieves competitive optimality rates in the setting where the number of actions is small. We finalize our results introducing a statistical gap fleshing out the fundamental differences between planning and adaptive learning and provide results for planning with model selection.

Reinforcement Learning/Online

Canzhe Zhao, Ruofeng Yang, Baoxiang Wang, Xuezhou Zhang, Shuai Li

In this work, we study the low-rank MDPs with adversarially changed losses in the full-information feedback setting. In particular, the unknown transition probability kernel admits a low-rank matrix decomposition \citep{REPUCB22}, and the loss functions may change adversarially but are revealed to the learner at the end of each episode. We propose a policy optimization-based algorithm POLO, and we prove that it attains the $\widetilde{O}(K^{\frac{5}{6}}A^{\frac{1}{2}}d\ln(1+M)/(1-\gamma)^2)$ regret guarantee, where $d$ is rank of the transition kernel (and hence the dimension of the unknown representations), $A$ is the cardinality of the action space, $M$ is the cardinality of the model class that contains all the plausible representations, and $\gamma$ is the discounted factor. Notably, our algorithm is oracle-efficient and has a regret guarantee with no dependence on the size of potentially arbitrarily large state space. Furthermore, we also prove an $\Omega(\frac{\gamma^2}{1-\gamma} \sqrt{d A K})$ regret lower bound for this problem, showing that low-rank MDPs are statistically more difficult to learn than linear MDPs in the regret minimization setting. To the best of our knowledge, we present the first algorithm that interleaves representation learning, exploration, and exploitation to achieve the sublinear regret guarantee for RL with nonlinear function approximation and adversarial losses.

Optimization/Bilevel optimization

Yifan Yang, Peiyao Xiao, Kaiyi Ji

In this paper, we revisit the bilevel optimization problem, in which the upper-level objective function is generally nonconvex and the lower-level objective function is strongly convex. Although this type of problem has been studied extensively, it still remains an open question how to achieve an $\mathcal{O}(\epsilon^{-1.5})$ sample complexity in Hessian/Jacobian-free stochastic bilevel optimization without any second-order derivative computation. To fill this gap, we propose a novel Hessian/Jacobian-free bilevel optimizer named FdeHBO, which features a simple fully single-loop structure, a projection-aided finite-difference Hessian/Jacobian-vector approximation, and momentum-based updates. Theoretically, we show that FdeHBO requires $\mathcal{O}(\epsilon^{-1.5})$ iterations (each using $\mathcal{O}(1)$ samples and only first-order gradient information) to find an $\epsilon$-accurate stationary point. As far as we know, this is the first Hessian/Jacobian-free method with an $\mathcal{O}(\epsilon^{-1.5})$ sample complexity for nonconvex-strongly-convex stochastic bilevel optimization.

Miscellaneous Aspects of Machine Learning/Kernel methods

Petar Bevanda, Max Beier, Armin Lederer, Stefan Sosnowski, Eyke Hüllermeier, Sandra Hirche

Many machine learning approaches for decision making, such as reinforcement learning, rely on simulators or predictive models to forecast the time-evolution of quantities of interest, e.g., the state of an agent or the reward of a policy. Forecasts of such complex phenomena are commonly described by highly nonlinear dynamical systems, making their use in optimization-based decision-making challenging.Koopman operator theory offers a beneficial paradigm for addressing this problem by characterizing forecasts via linear time-invariant (LTI) ODEs, turning multi-step forecasts into sparse matrix multiplication.Though there exists a variety of learning approaches, they usually lack crucial learning-theoretic guarantees, making the behavior of the obtained models with increasing data and dimensionality unclear.We address the aforementioned by deriving a universal Koopman-invariant reproducing kernel Hilbert space (RKHS) that solely spans transformations into LTI dynamical systems. The resulting Koopman Kernel Regression (KKR) framework enables the use of statistical learning tools from function approximation for novel convergence results and generalization error bounds under weaker assumptions than existing work. Our experiments demonstrate superior forecasting performance compared to Koopman operator and sequential data predictors in RKHS.

Optimization/Bilevel optimization

Yuyang Qiu, Uday Shanbhag, Farzad Yousefian

Federated learning (FL) has emerged as an enabling framework for communication-efficient decentralized training. We study three broadly applicable problem classes in FL: (i) Nondifferentiable nonconvex federated optimization; (ii) Federated bilevel optimization; (iii) Federated minimax problems. Notably, in an implicit sense, both (ii) and (iii) are instances of (i). However, the hierarchical problems in (ii) and (iii) are often complicated by the absence of a closed-form expression for the implicit objective function. Unfortunately, research on these problems has been limited and afflicted by reliance on strong assumptions, including the need for differentiability and L-smoothness of the implicit function. We address this shortcoming by making the following contributions. In (i), by leveraging convolution-based smoothing and Clarke’s subdifferential calculus, we devise a randomized smoothing-enabled zeroth-order FL method and derive communication and iteration complexity guarantees for computing an approximate Clarke stationary point. To contend with (ii) and (iii), we devise a unified randomized implicit zeroth-order FL framework, equipped with explicit communication and iteration complexities. Importantly, our method utilizes delays during local steps to skip making calls to the inexact lower-level FL oracle. This results in significant reduction in communication overhead when addressing hierarchical problems. We empirically validate the theory on nonsmooth and hierarchical ML problems.

Theory/Online Learning and Bandits

Zhiyu Zhang, Ashok Cutkosky, Yannis Paschalidis

Motivated by the challenge of nonstationarity in sequential decision making, we study Online Convex Optimization (OCO) under the coupling of two problem structures: the domain is unbounded, and the comparator sequence $u_1,\ldots,u_T$ is arbitrarily time-varying. As no algorithm can guarantee low regret simultaneously against all comparator sequences, handling this setting requires moving from minimax optimality to comparator adaptivity. That is, sensible regret bounds should depend on certain complexity measures of the comparator relative to one's prior knowledge. This paper achieves a new type of such adaptive regret bounds leveraging a sparse coding framework. The complexity of the comparator is measured by its energy and its sparsity on a user-specified dictionary, which offers considerable versatility. For example, equipped with a wavelet dictionary, our framework improves the state-of-the-art bound (Jacobsen & Cutkosky, 2022) by adapting to both ($i$) the magnitude of the comparator average $||\bar u||=||\sum_{t=1}^Tu_t/T||$, rather than the maximum $\max_t||u_t||$; and ($ii$) the comparator variability $\sum_{t=1}^T||u_t-\bar u||$, rather than the uncentered sum $\sum_{t=1}^T||u_t||$. Furthermore, our proof is simpler due to decoupling function approximation from regret minimization.

Deep Learning/Theory

TUNG LE, Remi Gribonval, Elisa Riccietti

Given a training set, a loss function, and a neural network architecture, it is often taken for granted that optimal network parameters exist, and a common practice is to apply available optimization algorithms to search for them. In this work, we show that the existence of an optimal solution is not always guaranteed, especially in the context of sparse ReLU neural networks.In particular, we first show that optimization problems involving deep networks with certain sparsity patterns do not always have optimal parameters, and that optimization algorithms may then diverge. Via a new topological relation between sparse ReLU neural networks and their linear counterparts, we derive --using existing tools from real algebraic geometry-- an algorithm to verify that a given sparsity pattern suffers from this issue. Then, the existence of a global optimum is proved for every concrete optimization problem involving a shallow sparse ReLU neural network of output dimension one. Overall, the analysis is based on the investigation of two topological properties of the space of functions implementable as sparse ReLU neural networks: a best approximation property, and a closedness property, both in the uniform norm. This is studied both for (finite) domains corresponding to practical training on finite training sets, and for more general domains such as the unit cube. This allows us to provide conditions for the guaranteed existence of an optimum given a sparsity pattern. The results apply not only to several sparsity patterns proposed in recent works on network pruning/sparsification, but also to classical dense neural networks, including architectures not covered by existing results.

Social Aspects/Trustworthy Machine Learning

Zhijin Ge, Hongying Liu, Wang Xiaosen, Fanhua Shang, Yuanyuan Liu

Transfer-based attack adopts the adversarial examples generated on the surrogate model to attack various models, making it applicable in the physical world and attracting increasing interest. Recently, various adversarial attacks have emerged to boost adversarial transferability from different perspectives. In this work, inspired by the observation that flat local minima are correlated with good generalization, we assume and empirically validate that adversarial examples at a flat local region tend to have good transferability by introducing a penalized gradient norm to the original loss function. Since directly optimizing the gradient regularization norm is computationally expensive and intractable for generating adversarial examples, we propose an approximation optimization method to simplify the gradient update of the objective function. Specifically, we randomly sample an example and adopt a first-order procedure to approximate the curvature of the second-order Hessian matrix, which makes computing more efficient by interpolating two Jacobian matrices. Meanwhile, in order to obtain a more stable gradient direction, we randomly sample multiple examples and average the gradients of these examples to reduce the variance due to random sampling during the iterative process. Extensive experimental results on the ImageNet-compatible dataset show that the proposed method can generate adversarial examples at flat local regions, and significantly improve the adversarial transferability on either normally trained models or adversarially trained models than the state-of-the-art attacks. Our codes are available at: https://github.com/Trustworthy-AI-Group/PGN.

Shenao Zhang, Boyi Liu, Zhaoran Wang, Tuo Zhao

ReParameterization (RP) Policy Gradient Methods (PGMs) have been widely adopted for continuous control tasks in robotics and computer graphics. However, recent studies have revealed that, when applied to long-term reinforcement learning problems, model-based RP PGMs may experience chaotic and non-smooth optimization landscapes with exploding gradient variance, which leads to slow convergence. This is in contrast to the conventional belief that reparameterization methods have low gradient estimation variance in problems such as training deep generative models. To comprehend this phenomenon, we conduct a theoretical examination of model-based RP PGMs and search for solutions to the optimization difficulties. Specifically, we analyze the convergence of the model-based RP PGMs and pinpoint the smoothness of function approximators as a major factor that affects the quality of gradient estimation. Based on our analysis, we propose a spectral normalization method to mitigate the exploding variance issue caused by long model unrolls. Our experimental results demonstrate that proper normalization significantly reduces the gradient variance of model-based RP PGMs. As a result, the performance of the proposed method is comparable or superior to other gradient estimators, such as the Likelihood Ratio (LR) gradient estimator. Our code is available at https://github.com/agentification/RP_PGM.