Daily Papers

Model merging has emerged as a promising approach for multi-task learning (MTL), offering a data-efficient alternative to conventional fine-tuning. However, with the rapid development of the open-source AI ecosystem and the increasing availability of fine-tuned foundation models, existing model merging methods face two key limitations: (i) They are primarily designed for in-house fine-tuned models, making them less adaptable to diverse model sources with partially unknown model and task information, (ii) They struggle to scale effectively when merging numerous model checkpoints. To address these challenges, we formulate model merging as a constrained optimization problem and introduce a novel approach: Frank-Wolfe Merging (FW-Merging). Inspired by Frank-Wolfe optimization, our approach iteratively selects the most relevant model in the pool to minimize a linear approximation of the objective function and then executes a local merging similar to the Frank-Wolfe update. The objective function is designed to capture the desired behavior of the target-merged model, while the fine-tuned candidate models define the constraint set. More importantly, FW-Merging serves as an orthogonal technique for existing merging methods, seamlessly integrating with them to further enhance accuracy performance. Our experiments show that FW-Merging scales across diverse model sources, remaining stable with 16 irrelevant models and improving by 15.3% with 16 relevant models on 20 CV tasks, while maintaining constant memory overhead, unlike the linear overhead of data-informed merging methods. Compared with the state-of-the-art approaches, FW-Merging surpasses the data-free merging method by 32.8% and outperforms the data-informed Adamerging by 8.39% when merging 20 ViT models. Our code is open-sourced at github.com/hmarkc/FW-Merging.

Generalized self-concordance is a key property present in the objective function of many important learning problems. We establish the convergence rate of a simple Frank-Wolfe variant that uses the open-loop step size strategy gamma_t = 2/(t+2), obtaining a O(1/t) convergence rate for this class of functions in terms of primal gap and Frank-Wolfe gap, where t is the iteration count. This avoids the use of second-order information or the need to estimate local smoothness parameters of previous work. We also show improved convergence rates for various common cases, e.g., when the feasible region under consideration is uniformly convex or polyhedral.

Dictionary learning is a widely used unsupervised learning method in signal processing and machine learning. Most existing works of dictionary learning are in an offline manner. There are mainly two offline ways for dictionary learning. One is to do an alternative optimization of both the dictionary and the sparse code; the other way is to optimize the dictionary by restricting it over the orthogonal group. The latter one is called orthogonal dictionary learning which has a lower complexity implementation, hence, it is more favorable for lowcost devices. However, existing schemes on orthogonal dictionary learning only work with batch data and can not be implemented online, which is not applicable for real-time applications. This paper proposes a novel online orthogonal dictionary scheme to dynamically learn the dictionary from streaming data without storing the historical data. The proposed scheme includes a novel problem formulation and an efficient online algorithm design with convergence analysis. In the problem formulation, we relax the orthogonal constraint to enable an efficient online algorithm. In the algorithm design, we propose a new Frank-Wolfe-based online algorithm with a convergence rate of O(ln t/t^(1/4)). The convergence rate in terms of key system parameters is also derived. Experiments with synthetic data and real-world sensor readings demonstrate the effectiveness and efficiency of the proposed online orthogonal dictionary learning scheme.

This paper focuses on the problem of constrained stochastic optimization. A zeroth order Frank-Wolfe algorithm is proposed, which in addition to the projection-free nature of the vanilla Frank-Wolfe algorithm makes it gradient free. Under convexity and smoothness assumption, we show that the proposed algorithm converges to the optimal objective function at a rate Oleft(1/T^{1/3}right), where T denotes the iteration count. In particular, the primal sub-optimality gap is shown to have a dimension dependence of Oleft(d^{1/3}right), which is the best known dimension dependence among all zeroth order optimization algorithms with one directional derivative per iteration. For non-convex functions, we obtain the Frank-Wolfe gap to be Oleft(d^{1/3}T^{-1/4}right). Experiments on black-box optimization setups demonstrate the efficacy of the proposed algorithm.

This paper introduces unified projection-free Frank-Wolfe type algorithms for adversarial continuous DR-submodular optimization, spanning scenarios such as full information and (semi-)bandit feedback, monotone and non-monotone functions, different constraints, and types of stochastic queries. For every problem considered in the non-monotone setting, the proposed algorithms are either the first with proven sub-linear alpha-regret bounds or have better alpha-regret bounds than the state of the art, where alpha is a corresponding approximation bound in the offline setting. In the monotone setting, the proposed approach gives state-of-the-art sub-linear alpha-regret bounds among projection-free algorithms in 7 of the 8 considered cases while matching the result of the remaining case. Additionally, this paper addresses semi-bandit and bandit feedback for adversarial DR-submodular optimization, advancing the understanding of this optimization area.

Maximizing a monotone submodular function is a fundamental task in machine learning, economics, and statistics. In this paper, we present two communication-efficient decentralized online algorithms for the monotone continuous DR-submodular maximization problem, both of which reduce the number of per-function gradient evaluations and per-round communication complexity from T^{3/2} to 1. The first one, One-shot Decentralized Meta-Frank-Wolfe (Mono-DMFW), achieves a (1-1/e)-regret bound of O(T^{4/5}). As far as we know, this is the first one-shot and projection-free decentralized online algorithm for monotone continuous DR-submodular maximization. Next, inspired by the non-oblivious boosting function zhang2022boosting, we propose the Decentralized Online Boosting Gradient Ascent (DOBGA) algorithm, which attains a (1-1/e)-regret of O(T). To the best of our knowledge, this is the first result to obtain the optimal O(T) against a (1-1/e)-approximation with only one gradient inquiry for each local objective function per step. Finally, various experimental results confirm the effectiveness of the proposed methods.

This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural optimization and stochastic optimization. Our presentation of black-box optimization, strongly influenced by Nesterov's seminal book and Nemirovski's lecture notes, includes the analysis of cutting plane methods, as well as (accelerated) gradient descent schemes. We also pay special attention to non-Euclidean settings (relevant algorithms include Frank-Wolfe, mirror descent, and dual averaging) and discuss their relevance in machine learning. We provide a gentle introduction to structural optimization with FISTA (to optimize a sum of a smooth and a simple non-smooth term), saddle-point mirror prox (Nemirovski's alternative to Nesterov's smoothing), and a concise description of interior point methods. In stochastic optimization we discuss stochastic gradient descent, mini-batches, random coordinate descent, and sublinear algorithms. We also briefly touch upon convex relaxation of combinatorial problems and the use of randomness to round solutions, as well as random walks based methods.

Fine-tuning is the primary methodology for tailoring pre-trained large language models to specific tasks. As the model's scale and the diversity of tasks expand, parameter-efficient fine-tuning methods are of paramount importance. One of the most widely used family of methods is low-rank adaptation (LoRA) and its variants. LoRA encodes weight update as the product of two low-rank matrices. Despite its advantages, LoRA falls short of full-parameter fine-tuning in terms of generalization error for certain tasks. We introduce Chain of LoRA (COLA), an iterative optimization framework inspired by the Frank-Wolfe algorithm, to bridge the gap between LoRA and full parameter fine-tuning, without incurring additional computational costs or memory overheads. COLA employs a residual learning procedure where it merges learned LoRA modules into the pre-trained language model parameters and re-initilize optimization for new born LoRA modules. We provide theoretical convergence guarantees as well as empirical results to validate the effectiveness of our algorithm. Across various models (OPT and llama-2) and seven benchmarking tasks, we demonstrate that COLA can consistently outperform LoRA without additional computational or memory costs.

We introduce CAMRL, the first curriculum-based asymmetric multi-task learning (AMTL) algorithm for dealing with multiple reinforcement learning (RL) tasks altogether. To mitigate the negative influence of customizing the one-off training order in curriculum-based AMTL, CAMRL switches its training mode between parallel single-task RL and asymmetric multi-task RL (MTRL), according to an indicator regarding the training time, the overall performance, and the performance gap among tasks. To leverage the multi-sourced prior knowledge flexibly and to reduce negative transfer in AMTL, we customize a composite loss with multiple differentiable ranking functions and optimize the loss through alternating optimization and the Frank-Wolfe algorithm. The uncertainty-based automatic adjustment of hyper-parameters is also applied to eliminate the need of laborious hyper-parameter analysis during optimization. By optimizing the composite loss, CAMRL predicts the next training task and continuously revisits the transfer matrix and network weights. We have conducted experiments on a wide range of benchmarks in multi-task RL, covering Gym-minigrid, Meta-world, Atari video games, vision-based PyBullet tasks, and RLBench, to show the improvements of CAMRL over the corresponding single-task RL algorithm and state-of-the-art MTRL algorithms. The code is available at: https://github.com/huanghanchi/CAMRL

AI Infrastructure plays a key role in the speed and cost-competitiveness of developing and deploying advanced AI models. The current demand for powerful AI infrastructure for model training is driven by the emergence of generative AI and foundational models, where on occasion thousands of GPUs must cooperate on a single training job for the model to be trained in a reasonable time. Delivering efficient and high-performing AI training requires an end-to-end solution that combines hardware, software and holistic telemetry to cater for multiple types of AI workloads. In this report, we describe IBM's hybrid cloud infrastructure that powers our generative AI model development. This infrastructure includes (1) Vela: an AI-optimized supercomputing capability directly integrated into the IBM Cloud, delivering scalable, dynamic, multi-tenant and geographically distributed infrastructure for large-scale model training and other AI workflow steps and (2) Blue Vela: a large-scale, purpose-built, on-premises hosting environment that is optimized to support our largest and most ambitious AI model training tasks. Vela provides IBM with the dual benefit of high performance for internal use along with the flexibility to adapt to an evolving commercial landscape. Blue Vela provides us with the benefits of rapid development of our largest and most ambitious models, as well as future-proofing against the evolving model landscape in the industry. Taken together, they provide IBM with the ability to rapidly innovate in the development of both AI models and commercial offerings.