Causal Discovery by Kernel Deviance Measures with Heterogeneous Transforms

The discovery of causal relationships in a set of random variables is a fundamental objective of science and has also recently been argued as being an essential component towards real machine intelligence. One class of causal discovery techniques are founded based on the argument that there are inherent structural asymmetries between the causal and anti-causal direction which could be leveraged in determining the direction of causation. To go about capturing these discrepancies between cause and effect remains to be a challenge and many current state-of-the-art algorithms propose to compare the norms of the kernel mean embeddings of the conditional distributions. In this work, we argue that such approaches based on RKHS embeddings are insufficient in capturing principal markers of cause-effect asymmetry involving higher-order structural variabilities of the conditional distributions. We propose Kernel Intrinsic Invariance Measure with Heterogeneous Transform (KIIM-HT) which introduces a novel score measure based on heterogeneous transformation of RKHS embeddings to extract relevant higher-order moments of the conditional densities for causal discovery. Inference is made via comparing the score of each hypothetical cause-effect direction. Tests and comparisons on a synthetic dataset, a two-dimensional synthetic dataset and the real-world benchmark dataset T\"ubingen Cause-Effect Pairs verify our approach. In addition, we conduct a sensitivity analysis to the regularization parameter to faithfully compare previous work to our method and an experiment with trials on varied hyperparameter values to showcase the robustness of our algorithm.

Causal Coordinated Concurrent Reinforcement Learning

In this work, we propose a novel algorithmic framework for data sharing and coordinated exploration for the purpose of learning more data-efficient and better performing policies under a concurrent reinforcement learning (CRL) setting. In contrast to other work which make the assumption that all agents act under identical environments, we relax this restriction and instead consider the formulation where each agent acts within an environment which shares a global structure but also exhibits individual variations. Our algorithm leverages a causal inference algorithm in the form of Additive Noise Model - Mixture Model (ANM-MM) in extracting model parameters governing individual differentials via independence enforcement. We propose a new data sharing scheme based on a similarity measure of the extracted model parameters and demonstrate superior learning speeds on a set of autoregressive, pendulum and cart-pole swing-up tasks and finally, we show the effectiveness of diverse action selection between common agents under a sparse reward setting. To the best of our knowledge, this is the first work in considering non-identical environments in CRL and one of the few works which seek to integrate causal inference with reinforcement learning (RL).

Efficient Robust Bayesian Optimization for Arbitrary Uncertain Inputs

Bayesian Optimization (BO) is a sample-efficient optimization algorithm widely employed across various applications. In some challenging BO tasks, input uncertainty arises due to the inevitable randomness in the optimization process, such as machining errors, execution noise, or contextual variability. This uncertainty deviates the input from the intended value before evaluation, resulting in significant performance fluctuations in the final result. In this paper, we introduce a novel robust Bayesian Optimization algorithm, AIRBO, which can effectively identify a robust optimum that performs consistently well under arbitrary input uncertainty. Our method directly models the uncertain inputs of arbitrary distributions by empowering the Gaussian Process with the Maximum Mean Discrepancy (MMD) and further accelerates the posterior inference via Nystrom approximation. Rigorous theoretical regret bound is established under MMD estimation error and extensive experiments on synthetic functions and real problems demonstrate that our approach can handle various input uncertainties and achieve state-of-the-art performance.

Efficient Robust Bayesian Optimization for Arbitrary Uncertain inputs

Bayesian Optimization (BO) is a sample-efficient optimization algorithm widely employed across various applications. In some challenging BO tasks, input uncertainty arises due to the inevitable randomness in the optimization process, such as machining errors, execution noise, or contextual variability. This uncertainty deviates the input from the intended value before evaluation, resulting in significant performance fluctuations in the final result. In this paper, we introduce a novel robust Bayesian Optimization algorithm, AIRBO, which can effectively identify a robust optimum that performs consistently well under arbitrary input uncertainty. Our method directly models the uncertain inputs of arbitrary distributions by empowering the Gaussian Process with the Maximum Mean Discrepancy (MMD) and further accelerates the posterior inference via Nystrom approximation. Rigorous theoretical regret bound is established under MMD estimation error and extensive experiments on synthetic functions and real problems demonstrate that our approach can handle various input uncertainties and achieve state-of-the-art performance.

Convergence guarantee for consistency models

We provide the first convergence guarantees for the Consistency Models (CMs), a newly emerging type of one-step generative models that can generate comparable samples to those generated by Diffusion Models. Our main result is that, under the basic assumptions on score-matching errors, consistency errors and smoothness of the data distribution, CMs can efficiently sample from any realistic data distribution in one step with small $W_2$ error. Our results (1) hold for $L^2$-accurate score and consistency assumption (rather than $L^\infty$-accurate); (2) do note require strong assumptions on the data distribution such as log-Sobelev inequality; (3) scale polynomially in all parameters; and (4) match the state-of-the-art convergence guarantee for score-based generative models (SGMs). We also provide the result that the Multistep Consistency Sampling procedure can further reduce the error comparing to one step sampling, which support the original statement of "Consistency Models, Yang Song 2023". Our result further imply a TV error guarantee when take some Langevin-based modifications to the output distributions.

Efficient Bayesian Optimization with Deep Kernel Learning and Transformer Pre-trained on Multiple Heterogeneous Datasets

Bayesian optimization (BO) is widely adopted in black-box optimization problems and it relies on a surrogate model to approximate the black-box response function. With the increasing number of black-box optimization tasks solved and even more to solve, the ability to learn from multiple prior tasks to jointly pre-train a surrogate model is long-awaited to further boost optimization efficiency. In this paper, we propose a simple approach to pre-train a surrogate, which is a Gaussian process (GP) with a kernel defined on deep features learned from a Transformer-based encoder, using datasets from prior tasks with possibly heterogeneous input spaces. In addition, we provide a simple yet effective mix-up initialization strategy for input tokens corresponding to unseen input variables and therefore accelerate new tasks' convergence. Experiments on both synthetic and real benchmark problems demonstrate the effectiveness of our proposed pre-training and transfer BO strategy over existing methods.

Reweighted Interacting Langevin Diffusions: an Accelerated Sampling Methodfor Optimization

We proposed a new technique to accelerate sampling methods for solving difficult optimization problems. Our method investigates the intrinsic connection between posterior distribution sampling and optimization with Langevin dynamics, and then we propose an interacting particle scheme that approximates a Reweighted Interacting Langevin Diffusion system (RILD). The underlying system is designed by adding a multiplicative source term into the classical Langevin operator, leading to a higher convergence rate and a more concentrated invariant measure. We analyze the convergence rate of our algorithm and the improvement compared to existing results in the asymptotic situation. We also design various tests to verify our theoretical results, showing the advantages of accelerating convergence and breaking through barriers of suspicious local minimums, especially in high-dimensional non-convex settings. Our algorithms and analysis shed some light on combining gradient and genetic algorithms using Partial Differential Equations (PDEs) with provable guarantees.

Neighbor Auto-Grouping Graph Neural Networks for Handover Parameter Configuration in Cellular Network

The mobile communication enabled by cellular networks is the one of the main foundations of our modern society. Optimizing the performance of cellular networks and providing massive connectivity with improved coverage and user experience has a considerable social and economic impact on our daily life. This performance relies heavily on the configuration of the network parameters. However, with the massive increase in both the size and complexity of cellular networks, network management, especially parameter configuration, is becoming complicated. The current practice, which relies largely on experts' prior knowledge, is not adequate and will require lots of domain experts and high maintenance costs. In this work, we propose a learning-based framework for handover parameter configuration. The key challenge, in this case, is to tackle the complicated dependencies between neighboring cells and jointly optimize the whole network. Our framework addresses this challenge in two ways. First, we introduce a novel approach to imitate how the network responds to different network states and parameter values, called auto-grouping graph convolutional network (AG-GCN). During the parameter configuration stage, instead of solving the global optimization problem, we design a local multi-objective optimization strategy where each cell considers several local performance metrics to balance its own performance and its neighbors. We evaluate our proposed algorithm via a simulator constructed using real network data. We demonstrate that the handover parameters our model can find, achieve better average network throughput compared to those recommended by experts as well as alternative baselines, which can bring better network quality and stability. It has the potential to massively reduce costs arising from human expert intervention and maintenance.

Reframed GES with a Neural Conditional Dependence Measure

In a nonparametric setting, the causal structure is often identifiable only up to Markov equivalence, and for the purpose of causal inference, it is useful to learn a graphical representation of the Markov equivalence class (MEC). In this paper, we revisit the Greedy Equivalence Search (GES) algorithm, which is widely cited as a score-based algorithm for learning the MEC of the underlying causal structure. We observe that in order to make the GES algorithm consistent in a nonparametric setting, it is not necessary to design a scoring metric that evaluates graphs. Instead, it suffices to plug in a consistent estimator of a measure of conditional dependence to guide the search. We therefore present a reframing of the GES algorithm, which is more flexible than the standard score-based version and readily lends itself to the nonparametric setting with a general measure of conditional dependence. In addition, we propose a neural conditional dependence (NCD) measure, which utilizes the expressive power of deep neural networks to characterize conditional independence in a nonparametric manner. We establish the optimality of the reframed GES algorithm under standard assumptions and the consistency of using our NCD estimator to decide conditional independence. Together these results justify the proposed approach. Experimental results demonstrate the effectiveness of our method in causal discovery, as well as the advantages of using our NCD measure over kernel-based measures.

Out-of-distribution Generalization with Causal Invariant Transformations

In real-world applications, it is important and desirable to learn a model that performs well on out-of-distribution (OOD) data. Recently, causality has become a powerful tool to tackle the OOD generalization problem, with the idea resting on the causal mechanism that is invariant across domains of interest. To leverage the generally unknown causal mechanism, existing works assume a linear form of causal feature or require sufficiently many and diverse training domains, which are usually restrictive in practice. In this work, we obviate these assumptions and tackle the OOD problem without explicitly recovering the causal feature. Our approach is based on transformations that modify the non-causal feature but leave the causal part unchanged, which can be either obtained from prior knowledge or learned from the training data in the multi-domain scenario. Under the setting of invariant causal mechanism, we theoretically show that if all such transformations are available, then we can learn a minimax optimal model across the domains using only single domain data. Noticing that knowing a complete set of these causal invariant transformations may be impractical, we further show that it suffices to know only a subset of these transformations. Based on the theoretical findings, a regularized training procedure is proposed to improve the OOD generalization capability. Extensive experimental results on both synthetic and real datasets verify the effectiveness of the proposed algorithm, even with only a few causal invariant transformations.