Obtaining Lower Query Complexities through Lightweight Zeroth-Order Proximal Gradient Algorithms

Zeroth-order (ZO) optimization is one key technique for machine learning problems where gradient calculation is expensive or impossible. Several variance reduced ZO proximal algorithms have been proposed to speed up ZO optimization for non-smooth problems, and all of them opted for the coordinated ZO estimator against the random ZO estimator when approximating the true gradient, since the former is more accurate. While the random ZO estimator introduces bigger error and makes convergence analysis more challenging compared to coordinated ZO estimator, it requires only $\mathcal{O}(1)$ computation, which is significantly less than $\mathcal{O}(d)$ computation of the coordinated ZO estimator, with $d$ being dimension of the problem space. To take advantage of the computationally efficient nature of the random ZO estimator, we first propose a ZO objective decrease (ZOOD) property which can incorporate two different types of errors in the upper bound of convergence rate. Next, we propose two generic reduction frameworks for ZO optimization which can automatically derive the convergence results for convex and non-convex problems respectively, as long as the convergence rate for the inner solver satisfies the ZOOD property. With the application of two reduction frameworks on our proposed ZOR-ProxSVRG and ZOR-ProxSAGA, two variance reduced ZO proximal algorithms with fully random ZO estimators, we improve the state-of-the-art function query complexities from $\mathcal{O}\left(\min\{\frac{dn^{1/2}}{\epsilon^2}, \frac{d}{\epsilon^3}\}\right)$ to $\tilde{\mathcal{O}}\left(\frac{n+d}{\epsilon^2}\right)$ under $d > n^{\frac{1}{2}}$ for non-convex problems, and from $\mathcal{O}\left(\frac{d}{\epsilon^2}\right)$ to $\tilde{\mathcal{O}}\left(n\log\frac{1}{\epsilon}+\frac{d}{\epsilon}\right)$ for convex problems.

Gradient-Free Method for Heavily Constrained Nonconvex Optimization

Zeroth-order (ZO) method has been shown to be a powerful method for solving the optimization problem where explicit expression of the gradients is difficult or infeasible to obtain. Recently, due to the practical value of the constrained problems, a lot of ZO Frank-Wolfe or projected ZO methods have been proposed. However, in many applications, we may have a very large number of nonconvex white/black-box constraints, which makes the existing zeroth-order methods extremely inefficient (or even not working) since they need to inquire function value of all the constraints and project the solution to the complicated feasible set. In this paper, to solve the nonconvex problem with a large number of white/black-box constraints, we proposed a doubly stochastic zeroth-order gradient method (DSZOG) with momentum method and adaptive step size. Theoretically, we prove DSZOG can converge to the $\epsilon$-stationary point of the constrained problem. Experimental results in two applications demonstrate the superiority of our method in terms of training time and accuracy compared with other ZO methods for the constrained problem.

Double Momentum Method for Lower-Level Constrained Bilevel Optimization

Bilevel optimization (BO) has recently gained prominence in many machine learning applications due to its ability to capture the nested structure inherent in these problems. Recently, many hypergradient methods have been proposed as effective solutions for solving large-scale problems. However, current hypergradient methods for the lower-level constrained bilevel optimization (LCBO) problems need very restrictive assumptions, namely, where optimality conditions satisfy the differentiability and invertibility conditions and lack a solid analysis of the convergence rate. What's worse, existing methods require either double-loop updates, which are sometimes less efficient. To solve this problem, in this paper, we propose a new hypergradient of LCBO leveraging the theory of nonsmooth implicit function theorem instead of using the restrive assumptions. In addition, we propose a \textit{single-loop single-timescale} algorithm based on the double-momentum method and adaptive step size method and prove it can return a $(\delta, \epsilon)$-stationary point with $\tilde{\mathcal{O}}(d_2^2\epsilon^{-4})$ iterations. Experiments on two applications demonstrate the effectiveness of our proposed method.

Hard-Thresholding Meets Evolution Strategies in Reinforcement Learning

Evolution Strategies (ES) have emerged as a competitive alternative for model-free reinforcement learning, showcasing exemplary performance in tasks like Mujoco and Atari. Notably, they shine in scenarios with imperfect reward functions, making them invaluable for real-world applications where dense reward signals may be elusive. Yet, an inherent assumption in ES, that all input features are task-relevant, poses challenges, especially when confronted with irrelevant features common in real-world problems. This work scrutinizes this limitation, particularly focusing on the Natural Evolution Strategies (NES) variant. We propose NESHT, a novel approach that integrates Hard-Thresholding (HT) with NES to champion sparsity, ensuring only pertinent features are employed. Backed by rigorous analysis and empirical tests, NESHT demonstrates its promise in mitigating the pitfalls of irrelevant features and shines in complex decision-making problems like noisy Mujoco and Atari tasks.

Is Next Token Prediction Sufficient for GPT? Exploration on Code Logic Comprehension

Large language models (LLMs) has experienced exponential growth, they demonstrate remarkable performance across various tasks. Notwithstanding, contemporary research primarily centers on enhancing the size and quality of pretraining data, still utilizing the next token prediction task on autoregressive transformer model structure. The efficacy of this task in truly facilitating the model's comprehension of code logic remains questionable, we speculate that it still interprets code as mere text, while human emphasizes the underlying logical knowledge. In order to prove it, we introduce a new task, "Logically Equivalent Code Selection," which necessitates the selection of logically equivalent code from a candidate set, given a query code. Our experimental findings indicate that current LLMs underperform in this task, since they understand code by unordered bag of keywords. To ameliorate their performance, we propose an advanced pretraining task, "Next Token Prediction+". This task aims to modify the sentence embedding distribution of the LLM without sacrificing its generative capabilities. Our experimental results reveal that following this pretraining, both Code Llama and StarCoder, the prevalent code domain pretraining models, display significant improvements on our logically equivalent code selection task and the code completion task.

Continuous Spiking Graph Neural Networks

Continuous graph neural networks (CGNNs) have garnered significant attention due to their ability to generalize existing discrete graph neural networks (GNNs) by introducing continuous dynamics. They typically draw inspiration from diffusion-based methods to introduce a novel propagation scheme, which is analyzed using ordinary differential equations (ODE). However, the implementation of CGNNs requires significant computational power, making them challenging to deploy on battery-powered devices. Inspired by recent spiking neural networks (SNNs), which emulate a biological inference process and provide an energy-efficient neural architecture, we incorporate the SNNs with CGNNs in a unified framework, named Continuous Spiking Graph Neural Networks (COS-GNN). We employ SNNs for graph node representation at each time step, which are further integrated into the ODE process along with time. To enhance information preservation and mitigate information loss in SNNs, we introduce the high-order structure of COS-GNN, which utilizes the second-order ODE for spiking representation and continuous propagation. Moreover, we provide the theoretical proof that COS-GNN effectively mitigates the issues of exploding and vanishing gradients, enabling us to capture long-range dependencies between nodes. Experimental results on graph-based learning tasks demonstrate the effectiveness of the proposed COS-GNN over competitive baselines.

FTBC: Forward Temporal Bias Correction for Optimizing ANN-SNN Conversion

Spiking Neural Networks (SNNs) offer a promising avenue for energy-efficient computing compared with Artificial Neural Networks (ANNs), closely mirroring biological neural processes. However, this potential comes with inherent challenges in directly training SNNs through spatio-temporal backpropagation -- stemming from the temporal dynamics of spiking neurons and their discrete signal processing -- which necessitates alternative ways of training, most notably through ANN-SNN conversion. In this work, we introduce a lightweight Forward Temporal Bias Correction (FTBC) technique, aimed at enhancing conversion accuracy without the computational overhead. We ground our method on provided theoretical findings that through proper temporal bias calibration the expected error of ANN-SNN conversion can be reduced to be zero after each time step. We further propose a heuristic algorithm for finding the temporal bias only in the forward pass, thus eliminating the computational burden of backpropagation and we evaluate our method on CIFAR-10/100 and ImageNet datasets, achieving a notable increase in accuracy on all datasets. Codes are released at a GitHub repository.

Federated Causal Discovery from Heterogeneous Data

Conventional causal discovery methods rely on centralized data, which is inconsistent with the decentralized nature of data in many real-world situations. This discrepancy has motivated the development of federated causal discovery (FCD) approaches. However, existing FCD methods may be limited by their potentially restrictive assumptions of identifiable functional causal models or homogeneous data distributions, narrowing their applicability in diverse scenarios. In this paper, we propose a novel FCD method attempting to accommodate arbitrary causal models and heterogeneous data. We first utilize a surrogate variable corresponding to the client index to account for the data heterogeneity across different clients. We then develop a federated conditional independence test (FCIT) for causal skeleton discovery and establish a federated independent change principle (FICP) to determine causal directions. These approaches involve constructing summary statistics as a proxy of the raw data to protect data privacy. Owing to the nonparametric properties, FCIT and FICP make no assumption about particular functional forms, thereby facilitating the handling of arbitrary causal models. We conduct extensive experiments on synthetic and real datasets to show the efficacy of our method. The code is available at https://github.com/lokali/FedCDH.git.

Limited Memory Online Gradient Descent for Kernelized Pairwise Learning with Dynamic Averaging

Pairwise learning, an important domain within machine learning, addresses loss functions defined on pairs of training examples, including those in metric learning and AUC maximization. Acknowledging the quadratic growth in computation complexity accompanying pairwise loss as the sample size grows, researchers have turned to online gradient descent (OGD) methods for enhanced scalability. Recently, an OGD algorithm emerged, employing gradient computation involving prior and most recent examples, a step that effectively reduces algorithmic complexity to $O(T)$, with $T$ being the number of received examples. This approach, however, confines itself to linear models while assuming the independence of example arrivals. We introduce a lightweight OGD algorithm that does not require the independence of examples and generalizes to kernel pairwise learning. Our algorithm builds the gradient based on a random example and a moving average representing the past data, which results in a sub-linear regret bound with a complexity of $O(T)$. Furthermore, through the integration of $O(\sqrt{T}{\log{T}})$ random Fourier features, the complexity of kernel calculations is effectively minimized. Several experiments with real-world datasets show that the proposed technique outperforms kernel and linear algorithms in offline and online scenarios.

DevEval: Evaluating Code Generation in Practical Software Projects

How to evaluate Large Language Models (LLMs) in code generation is an open question. Many benchmarks have been proposed but are inconsistent with practical software projects, e.g., unreal program distributions, insufficient dependencies, and small-scale project contexts. Thus, the capabilities of LLMs in practical projects are still unclear. In this paper, we propose a new benchmark named DevEval, aligned with Developers' experiences in practical projects. DevEval is collected through a rigorous pipeline, containing 2,690 samples from 119 practical projects and covering 10 domains. Compared to previous benchmarks, DevEval aligns to practical projects in multiple dimensions, e.g., real program distributions, sufficient dependencies, and enough-scale project contexts. We assess five popular LLMs on DevEval (e.g., gpt-4, gpt-3.5-turbo, CodeLLaMa, and StarCoder) and reveal their actual abilities in code generation. For instance, the highest Pass@1 of gpt-3.5-turbo only is 42 in our experiments. We also discuss the challenges and future directions of code generation in practical projects. We open-source DevEval and hope it can facilitate the development of code generation in practical projects.