arXiv subjects

Mohammad Pedramfar

Publications and source records attributed to Mohammad Pedramfar.

18 recordsLinked to original sources

arXiv2026

Dec-BFTRL: Squre-Root Regret for Decentralized Online Upper-Linearizable Optimization under Separation Access with Application to Continuous Submodular Maximization

We study decentralized online optimization of upper-linearizable payoffs over an action set under efficient separation access, with applications to online continuous diminishing-return (DR) submodular maximization. We propose Decentralized Barrier Follow-the-Regularized-Leader (Dec-BFTRL), and evaluate each agent's played action against the average of all local objectives. Each agent maps an internal iterate to a feasible action through an approximate gauge projection, communicates only a cumulative surrogate-gradient dual state, and invokes the local HybridNewton procedure to approximately minimize its post-communication BFTRL potential. For every agent, we achieve expected network-aggregate regret of $\widetilde O(\sqrt{T})$. Over $T$ rounds, each agent uses $T$ neighbor-mixing steps and $\widetilde O(T)$ separation-oracle calls. We give four wrapper instantiations covering three DR-submodular maximization problems.

math.OC↗

arXiv2026

Online Convex Optimization with Dueling Feedback

We study online convex optimization with dueling (pairwise comparison) feedback, where the learner observes only a binary preference between two queried points. While dueling feedback is well understood in discrete or stochastic settings, the adversarial convex setting has remained unexplored. We propose a simple reduction that converts dueling feedback into approximate gradients, enabling the use of standard first-order methods. We show that regret guarantees transfer under this reduction, yielding the first results for this setting, including $\mathcal{O}(T^{3/4})$ static, adaptive, and dynamic regret. Under additional structure, we obtain improved rates of $\mathcal{O}(T^{2/3})$ for smooth objectives and $\mathcal{O}(\sqrt{T \log T})$ for strongly convex functions.

cs.LG↗

arXiv2026

The Role of Symmetry in Optimizing Overparameterized Networks

Overparameterization is central to the success of deep learning, yet the mechanisms by which it improves optimization remain incompletely understood. We analyze weight-space symmetries in neural networks and show that overparameterization introduces additional symmetries that benefit optimization in two distinct ways. First, we prove that these symmetries act as a form of diagonal preconditioning on the Hessian, enabling the existence of better-conditioned minima within each equivalence class of functionally identical solutions. Second, we show that overparameterization increases the probability mass of global minima near typical initializations, making these favourable solutions more reachable. These results offer a potential link between loss landscape geometry and simplicity bias. Empirically, we observe wider networks have lower top eigenvalues, smaller condition numbers and faster convergence, matching our analysis. Our analysis provides a unified framework for understanding overparameterization and width growth as a geometric transformation of the loss landscape.

cs.LG↗

arXiv2026

Upper-Linearizability of Online Non-Monotone DR-Submodular Maximization over Down-Closed Convex Sets

We study online maximization of non-monotone Diminishing-Return(DR)-submodular functions over down-closed convex sets, a regime where existing projection-free online methods suffer from suboptimal regret and limited feedback guarantees. Our main contribution is a new structural result showing that this class is $1/e$-linearizable under carefully designed exponential reparametrization, scaling parameter, and surrogate potential, enabling a reduction to online linear optimization. As a result, we obtain $O(T^{1/2})$ static regret with a single gradient query per round and unlock adaptive and dynamic regret guarantees, together with improved rates under semi-bandit, bandit, and zeroth-order feedback. Across all feedback models, our bounds strictly improve the state of the art.

cs.LG↗

arXiv2026

$\gamma$-weakly $\theta$-up-concavity: A Unified Framework for Non-Convex Optimization Beyond DR-Submodular and OSS Functions

Optimizing non-convex functions is a fundamental challenge across machine learning and combinatorial optimization. We introduce and study $\gamma$-weakly $\theta$-up-concavity, a novel first-order condition that characterizes a broad class of such functions. This condition provides a powerful unifying framework, strictly generalizing both DR-submodular and One-Sided Smooth (OSS) functions while capturing broader forms of scale-dependent curvature, including accumulating-then-diminishing returns and flat-start behavior. Our central theoretical contribution demonstrates that $\gamma$-weakly $\theta$-up-concave functions are upper-linearizable: for any feasible point, we can construct a linear surrogate whose gains provably approximate the original non-linear objective. A key technical contribution is a nonuniform upper-linearization argument yielding approximation coefficients that depend explicitly on the curvature parameters and the geometry of the feasible region. This linearizability yields immediate and unified approximation guarantees for a wide range of problems. Specifically, we obtain unified approximation guarantees for offline optimization as well as static and dynamic regret bounds in online settings via standard reductions to linear optimization. Moreover, our framework recovers the optimal approximation coefficient for DR-submodular maximization and improves existing approximation coefficients for OSS optimization, particularly over matroid constraints.

cs.LG↗

arXiv2025

Multi-Armed Sampling Problem and the End of Exploration

This paper introduces the framework of multi-armed sampling, which serves as the sampling counterpart to the optimization problem of multi-armed bandits. Our primary motivation is to rigorously examine the exploration-exploitation trade-off in the context of sampling. We systematically define plausible notions of regret for this framework and establish corresponding lower bounds. We then propose a simple algorithm that achieves near-optimal regret bounds. Our theoretical results suggest that, in contrast to optimization, sampling barely requires any exploration. To further connect our findings with those of multi-armed bandits, we define a continuous family of problems and associated regret measures that smoothly interpolate and unify multi-armed sampling and multi-armed bandit problems using a temperature parameter. We believe that the multi-armed sampling framework and our findings in this setting can play a foundational role in the study of sampling, including recent neural samplers, much like the role of multi-armed bandits in reinforcement learning. In particular, our work sheds light on the role of exploration (or lack thereof) and the convergence properties of algorithms for entropy-regularized reinforcement learning, fine-tuning of pretrained models and reinforcement learning with human feedback (RLHF).

cs.LG↗

arXiv2025

Diffusion Tree Sampling: Scalable inference-time alignment of diffusion models

Adapting a pretrained diffusion model to new objectives at inference time remains an open problem in generative modeling. Existing steering methods suffer from inaccurate value estimation, especially at high noise levels, which biases guidance. Moreover, information from past runs is not reused to improve sample quality, resulting in inefficient use of compute. Inspired by the success of Monte Carlo Tree Search, we address these limitations by casting inference-time alignment as a search problem that reuses past computations. We introduce a tree-based approach that samples from the reward-aligned target density by propagating terminal rewards back through the diffusion chain and iteratively refining value estimates with each additional generation. Our proposed method, Diffusion Tree Sampling (DTS), produces asymptotically exact samples from the target distribution in the limit of infinite rollouts, and its greedy variant, Diffusion Tree Search (DTS$^\star$), performs a global search for high reward samples. On MNIST and CIFAR-10 class-conditional generation, DTS matches the FID of the best-performing baseline with up to $10\times$ less compute. In text-to-image generation and language completion tasks, DTS$^\star$ effectively searches for high reward samples that match best-of-N with up to $5\times$ less compute. By reusing information from previous generations, we get an anytime algorithm that turns additional compute into steadily better samples, providing a scalable approach for inference-time alignment of diffusion models.

cs.LG↗

arXiv2025

BAGEL: Adversarially Constrained Online Convex Optimization under Separation Oracle Access

In adversarial Constrained Online Convex Optimization (COCO), a learner selects actions from a fixed convex set while seeking both low regret and low cumulative constraint violation (CCV) under time-varying constraints. We ask what performance is achievable when the action set is accessed through a Separation Oracle (SO), rather than an exact Projection Oracle (PO) or a Linear Optimization Oracle (LOO). We introduce $\mathtt{BAGEL}$, which combines a Lyapunov-weighted surrogate loss, blocked adaptive online gradient descent, and an infeasible-projection procedure implemented with an SO. For convex costs and any $\beta\in(0,1/2]$, $\mathtt{BAGEL}$ achieves $\mathcal{O}(T^{1-\beta})$ regret and $\mathcal{O}(T^{1-\beta}\log T)$ cumulative violation using $\widetilde{\mathcal{O}}((D/r)^2T^{2\beta})$ SO calls. At $\beta=1/2$, this gives $\mathcal{O}(\sqrt{T})$ regret and $\mathcal{O}(\sqrt{T}\log T)$ violation with a near-linear number of SO calls. The result is an access oracle based guarantee, with computational relevance depends on the geometry of the action set and the cost of implementing its SO.

cs.LG↗

arXiv2025

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.

math.OC↗

arXiv2024

From Linear to Linearizable Optimization: A Novel Framework with Applications to Stationary and Non-stationary DR-submodular Optimization

This paper introduces the notion of upper-linearizable/quadratizable functions, a class that extends concavity and DR-submodularity in various settings, including monotone and non-monotone cases over different convex sets. A general meta-algorithm is devised to convert algorithms for linear/quadratic maximization into ones that optimize upper-linearizable/quadratizable functions, offering a unified approach to tackling concave and DR-submodular optimization problems. The paper extends these results to multiple feedback settings, facilitating conversions between semi-bandit/first-order feedback and bandit/zeroth-order feedback, as well as between first/zeroth-order feedback and semi-bandit/bandit feedback. Leveraging this framework, new algorithms are derived using existing results as base algorithms for convex optimization, improving upon state-of-the-art results in various cases. Dynamic and adaptive regret guarantees are obtained for DR-submodular maximization, marking the first algorithms to achieve such guarantees in these settings. Notably, the paper achieves these advancements with fewer assumptions compared to existing state-of-the-art results, underscoring its broad applicability and theoretical contributions to non-convex optimization.

math.OC↗

arXiv2024

Unified Projection-Free Algorithms for Adversarial DR-Submodular Optimization

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 $α$-regret bounds or have better $α$-regret bounds than the state of the art, where $α$ is a corresponding approximation bound in the offline setting. In the monotone setting, the proposed approach gives state-of-the-art sub-linear $α$-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.

cs.LG↗

arXiv2024

A Unified Framework for Analyzing Meta-algorithms in Online Convex Optimization

In this paper, we analyze the problem of online convex optimization in different settings, including different feedback types (full-information/semi-bandit/bandit/etc) in either stochastic or non-stochastic setting and different notions of regret (static adversarial regret/dynamic regret/adaptive regret). This is done through a framework which allows us to systematically propose and analyze meta-algorithms for the various settings described above. We show that any algorithm for online linear optimization with deterministic gradient feedback against fully adaptive adversaries is an algorithm for online convex optimization. We also show that any such algorithm that requires full-information feedback may be transformed to an algorithm with semi-bandit feedback with comparable regret bound. We further show that algorithms that are designed for fully adaptive adversaries using deterministic semi-bandit feedback can obtain similar bounds using only stochastic semi-bandit feedback when facing oblivious adversaries. We use this to describe general meta-algorithms to convert first order algorithms to zeroth order algorithms with comparable regret bounds. Our framework allows us to analyze online optimization in various settings, recovers several results in the literature with a simplified proof technique, and provides new results.

cs.LG↗

arXiv2024

Improved Bayesian Regret Bounds for Thompson Sampling in Reinforcement Learning

In this paper, we prove the first Bayesian regret bounds for Thompson Sampling in reinforcement learning in a multitude of settings. We simplify the learning problem using a discrete set of surrogate environments, and present a refined analysis of the information ratio using posterior consistency. This leads to an upper bound of order $\widetilde{O}(H\sqrt{d_{l_1}T})$ in the time inhomogeneous reinforcement learning problem where $H$ is the episode length and $d_{l_1}$ is the Kolmogorov $l_1-$dimension of the space of environments. We then find concrete bounds of $d_{l_1}$ in a variety of settings, such as tabular, linear and finite mixtures, and discuss how how our results are either the first of their kind or improve the state-of-the-art.

stat.ML↗

arXiv2024

A Unified Approach for Maximizing Continuous DR-submodular Functions

This paper presents a unified approach for maximizing continuous DR-submodular functions that encompasses a range of settings and oracle access types. Our approach includes a Frank-Wolfe type offline algorithm for both monotone and non-monotone functions, with different restrictions on the general convex set. We consider settings where the oracle provides access to either the gradient of the function or only the function value, and where the oracle access is either deterministic or stochastic. We determine the number of required oracle accesses in all cases. Our approach gives new/improved results for nine out of the sixteen considered cases, avoids computationally expensive projections in two cases, with the proposed framework matching performance of state-of-the-art approaches in the remaining five cases. Notably, our approach for the stochastic function value-based oracle enables the first regret bounds with bandit feedback for stochastic DR-submodular functions.

cs.LG↗

arXiv2023

Coagent Networks Revisited

Coagent networks formalize the concept of arbitrary networks of stochastic agents that collaborate to take actions in a reinforcement learning environment. Prominent examples of coagent networks in action include approaches to hierarchical reinforcement learning (HRL), such as those using options, which attempt to address the exploration exploitation trade-off by introducing abstract actions at different levels by sequencing multiple stochastic networks within the HRL agents. We first provide a unifying perspective on the many diverse examples that fall under coagent networks. We do so by formalizing the rules of execution in a coagent network, enabled by the novel and intuitive idea of execution paths in a coagent network. Motivated by parameter sharing in the hierarchical option-critic architecture, we revisit the coagent network theory and achieve a much shorter proof of the policy gradient theorem using our idea of execution paths, without any assumption on how parameters are shared among coagents. We then generalize our setting and proof to include the scenario where coagents act asynchronously. This new perspective and theorem also lead to more mathematically accurate and performant algorithms than those in the existing literature. Lastly, by running nonstationary RL experiments, we survey the performance and properties of different generalizations of option-critic models.

cs.LG↗

arXiv2023

Learning-based Two-tiered Online Optimization of Region-wide Datacenter Resource Allocation

Online optimization of resource management for large-scale data centers and infrastructures to meet dynamic capacity reservation demands and various practical constraints (e.g., feasibility and robustness) is a very challenging problem. Mixed Integer Programming (MIP) approaches suffer from recognized limitations in such a dynamic environment, while learning-based approaches may face with prohibitively large state/action spaces. To this end, this paper presents a novel two-tiered online optimization to enable a learning-based Resource Allowance System (RAS). To solve optimal server-to-reservation assignment in RAS in an online fashion, the proposed solution leverages a reinforcement learning (RL) agent to make high-level decisions, e.g., how much resource to select from the Main Switch Boards (MSBs), and then a low-level Mixed Integer Linear Programming (MILP) solver to generate the local server-to-reservation mapping, conditioned on the RL decisions. We take into account fault tolerance, server movement minimization, and network affinity requirements and apply the proposed solution to large-scale RAS problems. To provide interpretability, we further train a decision tree model to explain the learned policies and to prune unreasonable corner cases at the low-level MILP solver, resulting in further performance improvement. Extensive evaluations show that our two-tiered solution outperforms baselines such as pure MIP solver by over $15\%$ while delivering $100\times$ speedup in computation.

cs.NI↗

arXiv2023

Stochastic Submodular Bandits with Delayed Composite Anonymous Bandit Feedback

This paper investigates the problem of combinatorial multiarmed bandits with stochastic submodular (in expectation) rewards and full-bandit delayed feedback, where the delayed feedback is assumed to be composite and anonymous. In other words, the delayed feedback is composed of components of rewards from past actions, with unknown division among the sub-components. Three models of delayed feedback: bounded adversarial, stochastic independent, and stochastic conditionally independent are studied, and regret bounds are derived for each of the delay models. Ignoring the problem dependent parameters, we show that regret bound for all the delay models is $\tilde{O}(T^{2/3} + T^{1/3} \nu)$ for time horizon $T$, where $\nu$ is a delay parameter defined differently in the three cases, thus demonstrating an additive term in regret with delay in all the three delay models. The considered algorithm is demonstrated to outperform other full-bandit approaches with delayed composite anonymous feedback.

cs.LG↗

arXiv2019

Hairy Cantor sets

We introduce a topological object, called hairy Cantor set, which in many ways enjoys the universal features of objects like Jordan curve, Cantor set, Cantor bouquet, hairy Jordan curve, etc. We give an axiomatic characterisation of hairy Cantor sets, and prove that any two such objects in the plane are ambiently homeomorphic. Hairy Cantor sets appear in the study of the dynamics of holomorphic maps with infinitely many renormalisation structures. They are employed to link the fundamental concepts of polynomial-like renormalisation by Douady-Hubbard with the arithmetic conditions obtained by Herman-Yoccoz in the study of the dynamics of analytic circle diffeomorphisms.

math.GN↗