arXiv subjects

Michael J. Neely

Publications and source records attributed to Michael J. Neely.

At least 19 recordsLinked to original sources

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

Automatic Link Selection in Multi-Channel Multiple Access with Link Failures

This paper focuses on the problem of automatic link selection in multi-channel multiple access control using bandit feedback. In particular, a controller assigns multiple users to multiple channels in a time-slotted system, where in each time slot, at most one user can be assigned to a given channel, and at most one channel can be assigned to a given user. Given that user $i$ is assigned to channel $j$, the transmission fails with a fixed unknown probability $1-q_{i,j}$. The assignments are made dynamically using success/failure feedback. The goal is to maximize the time-average utility, where we consider an arbitrary (possibly nonsmooth) concave, entrywise nondecreasing utility function. The first proposed algorithm has fast $\mathcal{O}(\sqrt{\log(T)/T})$ convergence. However, this algorithm requires solving a convex optimization problem within each iteration, which can be computationally expensive. The second algorithm has slower $\mathcal{O}(\sqrt[3]{\log(T)/T})$ convergence, while avoiding the costly inner optimization. Both of these algorithms are adaptive. In particular, the convergence guarantee holds for any interval of $T$ consecutive slots during which the success probabilities do not change. We further study several special cases. In the single-channel setting, we obtain both fast $\mathcal{O}(\sqrt{\log(T)/T})$ convergence and efficient implementation via a simpler adaptive mechanism. We also consider a UCB-based non-adaptive algorithm with max-weight-type decisions. Simulations highlight intriguing performance trade-offs and demonstrate rapid adaptation of the proposed adaptive schemes.

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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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arXiv2024

Opportunistic Learning for Markov Decision Systems with Application to Smart Robots

This paper presents an online method that learns optimal decisions for a discrete time Markov decision problem with an opportunistic structure. The state at time $t$ is a pair $(S(t),W(t))$ where $S(t)$ takes values in a finite set $\mathcal{S}$ of basic states, and $\{W(t)\}_{t=0}^{\infty}$ is an i.i.d. sequence of random vectors that affect the system and that have an unknown distribution. Every slot $t$ the controller observes $(S(t),W(t))$ and chooses a control action $A(t)$. The triplet $(S(t),W(t),A(t))$ determines a vector of costs and the transition probabilities for the next state $S(t+1)$. The goal is to minimize the time average of an objective function subject to additional time average cost constraints. We develop an algorithm that acts on a corresponding virtual system where $S(t)$ is replaced by a decision variable. An equivalence between virtual and actual systems is established by enforcing a collection of time averaged global balance equations. For any desired $ε>0$, we prove the algorithm achieves an $ε$-optimal solution on the virtual system with a convergence time of $O(1/ε^2)$. The actual system runs at the same time, its actions are informed by the virtual system, and its conditional transition probabilities and costs are proven to be the same as the virtual system at every instant of time. Also, its unconditional probabilities and costs are shown in simulation to closely match the virtual system. Our simulations consider online control of a robot that explores a region of interest. Objects with varying rewards appear and disappear and the robot learns what areas to explore and what objects to collect and deliver to a home base.

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arXiv2024

Adaptive Optimization for Stochastic Renewal Systems

This paper considers online optimization for a system that performs a sequence of back-to-back tasks. Each task can be processed in one of multiple processing modes that affect the duration of the task, the reward earned, and an additional vector of penalties (such as energy or cost). Let $A[k]$ be a random matrix of parameters that specifies the duration, reward, and penalty vector under each processing option for task $k$. The goal is to observe $A[k]$ at the start of each new task $k$ and then choose a processing mode for the task so that, over time, time average reward is maximized subject to time average penalty constraints. This is a \emph{renewal optimization problem} and is challenging because the probability distribution for the $A[k]$ sequence is unknown. Prior work shows that any algorithm that comes within $ε$ of optimality must have $Ω(1/ε^2)$ convergence time. The only known algorithm that can meet this bound operates without time average penalty constraints and uses a diminishing stepsize that cannot adapt when probabilities change. This paper develops a new algorithm that is adaptive and comes within $O(ε)$ of optimality for any interval of $Θ(1/ε^2)$ tasks over which probabilities are held fixed, regardless of probabilities before the start of the interval.

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arXiv2023

A Two-Player Resource-Sharing Game with Asymmetric Information

This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource. Additionally, there exists an information asymmetry where each player has knowledge of the reward realizations of different subsets of the resources. If both players choose the same resource, the reward is divided equally between them, whereas if they choose different resources, each player gains the full reward of the resource. We first implement the iterative best response algorithm to find an $ε$-approximate Nash equilibrium for this game. This method of finding a Nash equilibrium may not be desirable when players do not trust each other and place no assumptions on the incentives of the opponent. To handle this case, we solve the problem of maximizing the worst-case expected utility of the first player. The solution leads to counter-intuitive insights in certain special cases. To solve the general version of the problem, we develop an efficient algorithmic solution that combines online convex optimization and the drift-plus penalty technique.

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arXiv2022

Random Variables with Measurability Constraints with Application to Opportunistic Scheduling

This paper proves a representation theorem regarding sequences of random elements that take values in a Borel space and are measurable with respect to the sigma algebra generated by an arbitrary union of sigma algebras. This, together with a related representation theorem of Kallenberg, is used to characterize the set of multidimensional decision vectors in a discrete time stochastic control problem with measurability and causality constraints, including opportunistic scheduling problems for time-varying communication networks. A network capacity theorem for these systems is refined, without requiring an implicit and arbitrarily complex extension of the state space, by introducing two measurability assumptions and using a theory of constructible sets. An example that makes use of well known pathologies in descriptive set theory is given to show a nonmeasurable scheduling scheme can outperform all measurable scheduling schemes.

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arXiv2021

Repeated Games, Optimal Channel Capture, and Open Problems for Slotted Multiple Access

This paper revisits a classical problem of slotted multiple access with success, idle, and collision events on each slot. First, results of a 2-user multiple access game are reported. The game was conducted at the University of Southern California over multiple semesters and involved competitions between student-designed algorithms. An algorithm called 4-State was a consistent winner. This algorithm is analyzed and shown to have an optimal expected score when competing against an independent version of itself. The structure of 4-State motivates exploration of the open question of how to minimize the expected time to capture the channel for a $n$-user situation. It is assumed that the system delivers perfect feedback on the number of users who transmitted at the end of each slot. An efficient algorithm is developed and conjectured to have an optimal expected capture time for all positive integers $n$. Optimality is proven in the special cases $n \in \{1, 2, 3, 4, 6\}$ using a novel analytical technique that introduces virtual users with enhanced capabilities.

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arXiv2021

Fast Learning for Renewal Optimization in Online Task Scheduling

This paper considers online optimization of a renewal-reward system. A controller performs a sequence of tasks back-to-back. Each task has a random vector of parameters, called the task type vector, that affects the task processing options and also affects the resulting reward and time duration of the task. The probability distribution for the task type vector is unknown and the controller must learn to make efficient decisions so that time average reward converges to optimality. Prior work on such renewal optimization problems leaves open the question of optimal convergence time. This paper develops an algorithm with an optimality gap that decays like $O(1/\sqrt{k})$, where $k$ is the number of tasks processed. The same algorithm is shown to have faster $O(\log(k)/k)$ performance when the system satisfies a strong concavity property. The proposed algorithm uses an auxiliary variable that is updated according to a classic Robbins-Monro iteration. It makes online scheduling decisions at the start of each renewal frame based on this variable and on the observed task type. A matching converse is obtained for the strongly concave case by constructing an example system for which all algorithms have performance at best $Ω(\log(k)/k)$. A matching $Ω(1/\sqrt{k})$ converse is also shown for the general case without strong concavity.

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arXiv2020

A Low Complexity Algorithm with $O(\sqrt{T})$ Regret and $O(1)$ Constraint Violations for Online Convex Optimization with Long Term Constraints

This paper considers online convex optimization over a complicated constraint set, which typically consists of multiple functional constraints and a set constraint. The conventional online projection algorithm (Zinkevich, 2003) can be difficult to implement due to the potentially high computation complexity of the projection operation. In this paper, we relax the functional constraints by allowing them to be violated at each round but still requiring them to be satisfied in the long term. This type of relaxed online convex optimization (with long term constraints) was first considered in Mahdavi et al. (2012). That prior work proposes an algorithm to achieve $O(\sqrt{T})$ regret and $O(T^{3/4})$ constraint violations for general problems and another algorithm to achieve an $O(T^{2/3})$ bound for both regret and constraint violations when the constraint set can be described by a finite number of linear constraints. A recent extension in \citet{Jenatton16ICML} can achieve $O(T^{\max\{θ,1-θ\}})$ regret and $O(T^{1-θ/2})$ constraint violations where $θ\in (0,1)$. The current paper proposes a new simple algorithm that yields improved performance in comparison to prior works. The new algorithm achieves an $O(\sqrt{T})$ regret bound with $O(1)$ constraint violations.

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arXiv2020

A Converse Result on Convergence Time for Opportunistic Wireless Scheduling

This paper proves an impossibility result for stochastic network utility maximization for multi-user wireless systems, including multiple access and broadcast systems. Every time slot an access point observes the current channel states for each user and opportunistically selects a vector of transmission rates. Channel state vectors are assumed to be independent and identically distributed with an unknown probability distribution. The goal is to learn to make decisions over time that maximize a concave utility function of the running time average transmission rate of each user. Recently it was shown that a stochastic Frank-Wolfe algorithm converges to utility-optimality with an error of $O(\log(T)/T)$, where $T$ is the time the algorithm has been running. An existing $Ω(1/T)$ converse is known. The current paper improves the converse to $Ω(\log(T)/T)$, which matches the known achievability result. It does this by constructing a particular (simple) system for which no algorithm can achieve a better performance. The proof uses a novel reduction of the opportunistic scheduling problem to a problem of estimating a Bernoulli probability $p$ from independent and identically distributed samples. Along the way we refine a regret bound for Bernoulli estimation to show that, for any sequence of estimators, the set of values $p \in [0,1]$ under which the estimators perform poorly has measure at least $1/8$.

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arXiv2019

Reversible Models for Wireless Multi-Channel Multiple Access

This paper presents a network layer model for a wireless multiple access system with both persistent and non-persistent users. There is a single access point with multiple identical channels. Each user who wants to send a file first scans a subset of the channels to find one that is idle. If at least one idle channel is found, the user transmits a file over that channel. If no idle channel is found, a persistent user will repeat the access attempt at a later time, while a non-persistent user will leave. This is a useful mathematical model for "coffee shop" situations where a group of persistent users stay near an access point for an extended period of time while non-persistent users come and go. Users have heterogeneous activity behavior, file upload rates, and service durations. The system is a complex multi-dimensional Markov chain. The steady state probabilities are found by exploiting a latent reversibility property. This enables simple expressions for throughput and blocking probability.

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arXiv2019

Learning Aided Optimization for Energy Harvesting Devices with Outdated State Information

This paper considers utility optimal power control for energy harvesting wireless devices with a finite capacity battery. The distribution information of the underlying wireless environment and harvestable energy is unknown and only outdated system state information is known at the device controller. This scenario shares similarity with Lyapunov opportunistic optimization and online learning but is different from both. By a novel combination of Zinkevich's online gradient learning technique and the drift-plus-penalty technique from Lyapunov opportunistic optimization, this paper proposes a learning-aided algorithm that achieves utility within $O(ε)$ of the optimal, for any desired $ε>0$, by using a battery with an $O(1/ε)$ capacity. The proposed algorithm has low complexity and makes power investment decisions based on system history, without requiring knowledge of the system state or its probability distribution.

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arXiv2019

Online Primal-Dual Mirror Descent under Stochastic Constraints

We consider online convex optimization with stochastic constraints where the objective functions are arbitrarily time-varying and the constraint functions are independent and identically distributed (i.i.d.) over time. Both the objective and constraint functions are revealed after the decision is made at each time slot. The best known expected regret for solving such a problem is $\mathcal{O}(\sqrt{T})$, with a coefficient that is polynomial in the dimension of the decision variable and relies on the Slater condition (i.e. the existence of interior point assumption), which is restrictive and in particular precludes treating equality constraints. In this paper, we show that such Slater condition is in fact not needed. We propose a new primal-dual mirror descent algorithm and show that one can attain $\mathcal{O}(\sqrt{T})$ regret and constraint violation under a much weaker Lagrange multiplier assumption, allowing general equality constraints and significantly relaxing the previous Slater conditions. Along the way, for the case where decisions are contained in a probability simplex, we reduce the coefficient to have only a logarithmic dependence on the decision variable dimension. Such a dependence has long been known in the literature on mirror descent but seems new in this new constrained online learning scenario.

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arXiv2019

Opportunistic Scheduling over Renewal Systems: An Empirical Method

This paper considers an opportunistic scheduling problem over a renewal system. A controller observes a random event at the beginning of each renewal frame and then chooses an action in response to the event, which affects the duration of the frame, the amount of resources used, and a penalty metric. The goal is to make frame-wise decisions so as to minimize the time average penalty subject to time average resource constraints. This problem has applications to task processing and communication in data networks, as well as to certain classes of Markov decision problems. We formulate the problem as a dynamic fractional program and propose an adaptive algorithm which uses an empirical accumulation as a feedback parameter. A key feature of the proposed algorithm is that it does not require knowledge of the random event statistics and potentially allows (uncountably) infinite event sets. We prove the algorithm satisfies all desired constraints and achieves $O(ε)$ near optimality with probability 1.

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arXiv2018

Solving Non-smooth Constrained Programs with Lower Complexity than $\mathcal{O}(1/\varepsilon)$: A Primal-Dual Homotopy Smoothing Approach

We propose a new primal-dual homotopy smoothing algorithm for a linearly constrained convex program, where neither the primal nor the dual function has to be smooth or strongly convex. The best known iteration complexity solving such a non-smooth problem is $\mathcal{O}(\varepsilon^{-1})$. In this paper, we show that by leveraging a local error bound condition on the dual function, the proposed algorithm can achieve a better primal convergence time of $\mathcal{O}\left(\varepsilon^{-2/(2+β)}\log_2(\varepsilon^{-1})\right)$, where $β\in(0,1]$ is a local error bound parameter. As an example application of the general algorithm, we show that the distributed geometric median problem, which can be formulated as a constrained convex program, has its dual function non-smooth but satisfying the aforementioned local error bound condition with $β=1/2$, therefore enjoying a convergence time of $\mathcal{O}\left(\varepsilon^{-4/5}\log_2(\varepsilon^{-1})\right)$. This result improves upon the $\mathcal{O}(\varepsilon^{-1})$ convergence time bound achieved by existing distributed optimization algorithms. Simulation experiments also demonstrate the performance of our proposed algorithm.

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