Improving LoRA in Privacy-preserving Federated Learning

Low-rank adaptation (LoRA) is one of the most popular task-specific parameter-efficient fine-tuning (PEFT) methods on pre-trained language models for its good performance and computational efficiency. LoRA injects a product of two trainable rank decomposition matrices over the top of each frozen pre-trained model module. However, when applied in the setting of privacy-preserving federated learning (FL), LoRA may become unstable due to the following facts: 1) the effects of data heterogeneity and multi-step local updates are non-negligible, 2) additive noise enforced on updating gradients to guarantee differential privacy (DP) can be amplified and 3) the final performance is susceptible to hyper-parameters. A key factor leading to these phenomena is the discordance between jointly optimizing the two low-rank matrices by local clients and separately aggregating them by the central server. Thus, this paper proposes an efficient and effective version of LoRA, Federated Freeze A LoRA (FFA-LoRA), to alleviate these challenges and further halve the communication cost of federated fine-tuning LLMs. The core idea of FFA-LoRA is to fix the randomly initialized non-zero matrices and only fine-tune the zero-initialized matrices. Compared to LoRA, FFA-LoRA is motivated by practical and theoretical benefits in privacy-preserved FL. Our experiments demonstrate that FFA-LoRA provides more consistent performance with better computational efficiency over vanilla LoRA in various FL tasks.

Provably Fast Convergence of Independent Natural Policy Gradient for Markov Potential Games

This work studies an independent natural policy gradient (NPG) algorithm for the multi-agent reinforcement learning problem in Markov potential games. It is shown that, under mild technical assumptions and the introduction of the \textit{suboptimality gap}, the independent NPG method with an oracle providing exact policy evaluation asymptotically reaches an $\epsilon$-Nash Equilibrium (NE) within $\mathcal{O}(1/\epsilon)$ iterations. This improves upon the previous best result of $\mathcal{O}(1/\epsilon^2)$ iterations and is of the same order, $\mathcal{O}(1/\epsilon)$, that is achievable for the single-agent case. Empirical results for a synthetic potential game and a congestion game are presented to verify the theoretical bounds.

On the Stability Analysis of Open Federated Learning Systems

We consider the open federated learning (FL) systems, where clients may join and/or leave the system during the FL process. Given the variability of the number of present clients, convergence to a fixed model cannot be guaranteed in open systems. Instead, we resort to a new performance metric that we term the stability of open FL systems, which quantifies the magnitude of the learned model in open systems. Under the assumption that local clients' functions are strongly convex and smooth, we theoretically quantify the radius of stability for two FL algorithms, namely local SGD and local Adam. We observe that this radius relies on several key parameters, including the function condition number as well as the variance of the stochastic gradient. Our theoretical results are further verified by numerical simulations on both synthetic and real-world benchmark data-sets.

On Centralized and Distributed Mirror Descent: Exponential Convergence Analysis Using Quadratic Constraints

Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we study the exact convergence rate of MD in both centralized and distributed cases for strongly convex and smooth problems. We view MD with a dynamical system lens and leverage quadratic constraints (QCs) to provide convergence guarantees based on the Lyapunov stability. For centralized MD, we establish a semi-definite programming (SDP) that certifies exponentially fast convergence of MD subject to a linear matrix inequality (LMI). We prove that the SDP always has a feasible solution that recovers the optimal GD rate. Next, we analyze the exponential convergence of distributed MD and characterize the rate using two LMIs. To the best of our knowledge, the exact (exponential) rate of distributed MD has not been previously explored in the literature. We present numerical results as a verification of our theory and observe that the richness of the Lyapunov function entails better (worst-case) convergence rates compared to existing works on distributed GD.

Linear Convergence of Distributed Mirror Descent with Integral Feedback for Strongly Convex Problems

Distributed optimization often requires finding the minimum of a global objective function written as a sum of local functions. A group of agents work collectively to minimize the global function. We study a continuous-time decentralized mirror descent algorithm that uses purely local gradient information to converge to the global optimal solution. The algorithm enforces consensus among agents using the idea of integral feedback. Recently, Sun and Shahrampour (2020) studied the asymptotic convergence of this algorithm for when the global function is strongly convex but local functions are convex. Using control theory tools, in this work, we prove that the algorithm indeed achieves (local) exponential convergence. We also provide a numerical experiment on a real data-set as a validation of the convergence speed of our algorithm.

Distributed Mirror Descent with Integral Feedback: Asymptotic Convergence Analysis of Continuous-time Dynamics

This work addresses distributed optimization, where a network of agents wants to minimize a global strongly convex objective function. The global function can be written as a sum of local convex functions, each of which is associated with an agent. We propose a continuous-time distributed mirror descent algorithm that uses purely local information to converge to the global optimum. Unlike previous work on distributed mirror descent, we incorporate an integral feedback in the update, allowing the algorithm to converge with a constant step-size when discretized. We establish the asymptotic convergence of the algorithm using Lyapunov stability analysis. We further illustrate numerical experiments that verify the advantage of adopting integral feedback for improving the convergence rate of distributed mirror descent.

Can I trust you more? Model-Agnostic Hierarchical Explanations

Interactions such as double negation in sentences and scene interactions in images are common forms of complex dependencies captured by state-of-the-art machine learning models. We propose Mah\'e, a novel approach to provide Model-agnostic hierarchical \'explanations of how powerful machine learning models, such as deep neural networks, capture these interactions as either dependent on or free of the context of data instances. Specifically, Mah\'e provides context-dependent explanations by a novel local interpretation algorithm that effectively captures any-order interactions, and obtains context-free explanations through generalizing context-dependent interactions to explain global behaviors. Experimental results show that Mah\'e obtains improved local interaction interpretations over state-of-the-art methods and successfully explains interactions that are context-free.