Order-Optimal Projection-Free Algorithm for Adversarially Constrained Online Convex Optimization

Projection-based algorithms for constrained Online Convex Optimization (COCO) face scalability challenges in high-dimensional settings due to the computational complexity of projecting iterates onto constraint sets. This paper introduces a projection-free algorithm for COCO that achieves state-of-the-art performance guarantees while eliminating the need for projections. By integrating a separation oracle with adaptive Online Gradient Descent (OGD) and employing a Lyapunov-driven surrogate function, while dynamically adjusting step sizes using gradient norms, our method jointly optimizes the regret and cumulative constraint violation (CCV). We also use a blocked version of OGD that helps achieve tradeoffs betweeen the regret and CCV with the number of calls to the separation oracle. For convex cost functions, our algorithm attains an optimal regret of $\mathcal{O}(\sqrt{T})$ and a CCV of $\mathcal{O}(\sqrt{T} \log T)$, matching the best-known projection-based results, while only using $\tilde{\mathcal{O}}({T})$ calls to the separation oracle. The results also demonstrate a tradeoff where lower calls to the separation oracle increase the regret and the CCV. In the strongly convex setting, we further achieve a regret of $\mathcal{O}(\log T)$ and a CCV of $\mathcal{O}(\sqrt{T\log T} )$, while requiring ${\mathcal{O}}({T}^2)$ calls to the separation oracle. Further, tradeoff with the decreasing oracle calls is studied. These results close the gap between projection-free and projection-based approaches, demonstrating that projection-free methods can achieve performance comparable to projection-based counterparts.

Decentralized Projection-free Online Upper-Linearizable Optimization with Applications to DR-Submodular Optimization

We introduce a novel framework for decentralized projection-free optimization, extending projection-free methods to a broader class of upper-linearizable functions. Our approach leverages decentralized optimization techniques with the flexibility of upper-linearizable function frameworks, effectively generalizing traditional DR-submodular function optimization. We obtain the regret of $O(T^{1-\theta/2})$ with communication complexity of $O(T^{\theta})$ and number of linear optimization oracle calls of $O(T^{2\theta})$ for decentralized upper-linearizable function optimization, for any $0\le \theta \le 1$. This approach allows for the first results for monotone up-concave optimization with general convex constraints and non-monotone up-concave optimization with general convex constraints. Further, the above results for first order feedback are extended to zeroth order, semi-bandit, and bandit feedback.

Dendritic Localized Learning: Toward Biologically Plausible Algorithm

Backpropagation is the foundational algorithm for training neural networks and a key driver of deep learning's success. However, its biological plausibility has been challenged due to three primary limitations: weight symmetry, reliance on global error signals, and the dual-phase nature of training, as highlighted by the existing literature. Although various alternative learning approaches have been proposed to address these issues, most either fail to satisfy all three criteria simultaneously or yield suboptimal results. Inspired by the dynamics and plasticity of pyramidal neurons, we propose Dendritic Localized Learning (DLL), a novel learning algorithm designed to overcome these challenges. Extensive empirical experiments demonstrate that DLL satisfies all three criteria of biological plausibility while achieving state-of-the-art performance among algorithms that meet these requirements. Furthermore, DLL exhibits strong generalization across a range of architectures, including MLPs, CNNs, and RNNs. These results, benchmarked against existing biologically plausible learning algorithms, offer valuable empirical insights for future research. We hope this study can inspire the development of new biologically plausible algorithms for training multilayer networks and advancing progress in both neuroscience and machine learning.

FairEdit: Preserving Fairness in Graph Neural Networks through Greedy Graph Editing

Graph Neural Networks (GNNs) have proven to excel in predictive modeling tasks where the underlying data is a graph. However, as GNNs are extensively used in human-centered applications, the issue of fairness has arisen. While edge deletion is a common method used to promote fairness in GNNs, it fails to consider when data is inherently missing fair connections. In this work we consider the unexplored method of edge addition, accompanied by deletion, to promote fairness. We propose two model-agnostic algorithms to perform edge editing: a brute force approach and a continuous approximation approach, FairEdit. FairEdit performs efficient edge editing by leveraging gradient information of a fairness loss to find edges that improve fairness. We find that FairEdit outperforms standard training for many data sets and GNN methods, while performing comparably to many state-of-the-art methods, demonstrating FairEdit's ability to improve fairness across many domains and models.