arXiv subjects

Kamiar Asgari

Publications and source records attributed to Kamiar Asgari.

5 recordsLinked to original sources

arXiv2026

Optimal Regret for Online Storage Control via Cumulative Policies

We study online control of a scalar storage system with adversarial nonnegative arrivals, known retention coefficient, and convex costs depending on both state and action. Each action must respect current resource availability and is chosen before the current arrival and cost function are revealed. For the existing simplex disturbance-action policy class, we give an exact reparameterization by cumulative allocation fractions and a decay-weighted projected subgradient update. The resulting regret bound is independent of policy memory length. For fixed retention coefficient and cost constants, the controller achieves $O(\sqrt T)$ regret against the best fixed infinite-memory policy in this class, using $O(\log T)$ memory and arithmetic operations per round and one cost-subgradient query. A storage-specific block construction gives a matching lower bound against every causal feasible controller, including randomized controllers. Writing $τ=(1-α)^{-1}$, the minimax expected regret is $Θ(\sqrt T\min\{T,τ\}^{3/2})$ for every finite-memory simplex policy class and its infinite-memory extension, when $α\in[1/2,1)$, $T\ge4$, and the positive cost constants are fixed. This identifies the joint horizon and retention-time dependence for these policy benchmarks.

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arXiv2026

Projection-Free Non-Smooth Convex Programming

We study nonsmooth convex minimization over a compact convex set without projections. For a globally $L$-Lipschitz objective, optimistic primal-dual updates give error at most $2LD/\sqrt{T}$ after $T$ iterations, where $D$ is the set's diameter. Each iteration uses at most one linear optimization call and one subgradient query at a point that may lie outside the feasible set. For objectives that are $μ$-strongly convex on the feasible set, we present a direct method with error at most $32ρ^2L^2/[μ(T+1)]$. It uses a local linear optimization oracle with expansion factor $ρ$ and subgradients of norm at most $L$ queried only at feasible points. The method requires neither restarts nor advance knowledge of $T$. We give self-contained proofs and a short restart argument for the convex variant of the Garber-Hazan algorithm that removes the logarithmic factor from their error bound.

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arXiv2026

Online Constrained Control of Storage Systems via Simplex Disturbance-Action Policies

We study online control of a scalar storage system with nonnegative adversarial resource arrivals and state-dependent action constraints. The adversarial, time-varying cost depends on both state and action. At each time, the controller selects a feasible action before the current resource arrival and cost are revealed. To handle the coupling between feasibility and online learning, we introduce Simplex Disturbance-Action Control (SDAC), whose policies have $H$ nonnegative parameters summing to at most one. Every fixed SDAC policy is feasible by construction. Our online SDAC controller updates these parameters using entropic online mirror descent while preserving feasibility along the time-varying trajectory. We prove a regret bound of $O\!\left(\sqrt{T\log(H+1)}\right)$ relative to the best fixed SDAC policy and a minimax lower bound showing that the dependence on $T$ is tight. We also introduce infinite-memory SDAC policies, which include every feasible fixed-fraction policy. SDAC policies approximate this class with an error that decreases geometrically with $H$. For a suitable choice $H=Θ(\log T)$, the resulting regret against infinite-memory SDAC policies is $O\!\left(\sqrt{T\log\log T}\right)$. The framework applies to energy-harvesting batteries and other storage-constrained resource systems.

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arXiv2026

Bandit-Based Rate Adaptation for a Single-Server Queue

This paper considers the problem of obtaining bounded time-average expected queue sizes in a single-queue system with a partial-feedback structure. Time is slotted; in slot $t$ the transmitter chooses a rate $V(t)$ from a continuous interval. Transmission succeeds if and only if $V(t)\le C(t)$, where channel capacities $\{C(t)\}$ and arrivals are i.i.d. draws from fixed but unknown distributions. The transmitter observes only binary acknowledgments (ACK/NACK) indicating success or failure. Let $\varepsilon>0$ denote a sufficiently small lower bound on the slack between the arrival rate and the capacity region. We propose a phased algorithm that progressively refines a discretization of the uncountable infinite rate space and, without knowledge of $\varepsilon$, achieves a $\mathcal{O}\!\big(\log^{3.5}(1/\varepsilon)/\varepsilon^{3}\big)$ time-average expected queue size uniformly over the horizon. We also prove a converse result showing that for any rate-selection algorithm, regardless of whether $\varepsilon$ is known, there exists an environment in which the worst-case time-average expected queue size is $Ω(1/\varepsilon^{2})$. Thus, while a gap remains in the setting without knowledge of $\varepsilon$, we show that if $\varepsilon$ is known, a simple single-stage UCB type policy with a fixed discretization of the rate space achieves $\mathcal{O}\!\big(\log(1/\varepsilon)/\varepsilon^{2}\big)$, matching the converse up to logarithmic factors.

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arXiv2024

Nonsmooth Projection-Free Optimization with Functional Constraints

This paper presents a subgradient-based algorithm for constrained nonsmooth convex optimization that does not require projections onto the feasible set. While the well-established Frank-Wolfe algorithm and its variants already avoid projections, they are primarily designed for smooth objective functions. In contrast, our proposed algorithm can handle nonsmooth problems with general convex functional inequality constraints. It achieves an $ε$-suboptimal solution in $\mathcal{O}(ε^{-2})$ iterations, with each iteration requiring only a single (potentially inexact) Linear Minimization Oracle (LMO) call and a (possibly inexact) subgradient computation. This performance is consistent with existing lower bounds. Similar performance is observed when deterministic subgradients are replaced with stochastic subgradients. In the special case where there are no functional inequality constraints, our algorithm competes favorably with a recent nonsmooth projection-free method designed for constraint-free problems. Our approach utilizes a simple separation scheme in conjunction with a new Lagrange multiplier update rule.

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