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1. Efficient and Near-Optimal Online Portfolio Selection

   Jézéquel, R; Ostrovskii, D.; Gaillard, P. (October 2022, ArXivorg)

   In the problem of online portfolio selection as formulated by Cover (1991), the trader repeatedly distributes her capital over d assets in each of T>1 rounds, with the goal of maximizing the total return. Cover proposed an algorithm, termed Universal Portfolios, that performs nearly as well as the best (in hindsight) static assignment of a portfolio, with an O(dlog(T)) regret in terms of the logarithmic return. Without imposing any restrictions on the market this guarantee is known to be worst-case optimal, and no other algorithm attaining it has been discovered so far. Unfortunately, Cover's algorithm crucially relies on computing certain d-dimensional integral which must be approximated in any implementation; this results in a prohibitive O(d^4(T+d)^14) per-round runtime for the fastest known implementation due to Kalai and Vempala (2002). We propose an algorithm for online portfolio selection that admits essentially the same regret guarantee as Universal Portfolios -- up to a constant factor and replacement of log(T) with log(T+d) -- yet has a drastically reduced runtime of O(d^(T+d)) per round. The selected portfolio minimizes the current logarithmic loss regularized by the log-determinant of its Hessian -- equivalently, the hybrid logarithmic-volumetric barrier of the polytope specified by the asset return vectors. As such, our work reveals surprising connections of online portfolio selection with two classical topics in optimization theory: cutting-plane and interior-point algorithms. 

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2. Online Optimization in Cloud Resource Provisioning: Predictions, Regrets, and Algorithms

   Comden, Joshua; Yao, Sijie; Chen, Niangjun; Xing, Haipeng; Liu, Zhenhua (January 2019, Proceedings of the ACM on Measurement and Analysis of Computing Systems)

   Due to mainstream adoption of cloud computing and its rapidly increasing usage of energy, the efficient management of cloud computing resources has become an important issue. A key challenge in managing the resources lies in the volatility of their demand. While there have been a wide variety of online algorithms (e.g. Receding Horizon Control, Online Balanced Descent) designed, it is hard for cloud operators to pick the right algorithm. In particular, these algorithms vary greatly on their usage of predictions and performance guarantees. This paper aims at studying an automatic algorithm selection scheme in real time. To do this, we empirically study the prediction errors from real-world cloud computing traces. Results show that prediction errors are distinct from different prediction algorithms, across virtual machines, and over the time horizon. Based on these observations, we propose a simple prediction error model and prove upper bounds on the dynamic regret of several online algorithms. We then apply the empirical and theoretical results to create a simple online meta-algorithm that chooses the best algorithm on the fly. Numerical simulations demonstrate that the performance of the designed policy is close to that of the best algorithm in hindsight. 

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3. Generalization in portfolio-based algorithm selection

   Balcan, M.-F.; Sandholm, T.; Vitercik, E. (January 2021, Proceedings of the AAAI Conference on Artificial Intelligence)

   null (Ed.)

   Portfolio-based algorithm selection has seen tremendous practical success over the past two decades. This algorithm configuration procedure works by first selecting a portfolio of diverse algorithm parameter settings, and then, on a given problem instance, using an algorithm selector to choose a parameter setting from the portfolio with strong predicted performance. Oftentimes, both the portfolio and the algorithm selector are chosen using a training set of typical problem instances from the application domain at hand. In this paper, we provide the first provable guarantees for portfolio-based algorithm selection. We analyze how large the training set should be to ensure that the resulting algorithm selector's average performance over the training set is close to its future (expected) performance. This involves analyzing three key reasons why these two quantities may diverge: 1) the learning-theoretic complexity of the algorithm selector, 2) the size of the portfolio, and 3) the learning-theoretic complexity of the algorithm's performance as a function of its parameters. We introduce an end-to-end learning-theoretic analysis of the portfolio construction and algorithm selection together. We prove that if the portfolio is large, overfitting is inevitable, even with an extremely simple algorithm selector. With experiments, we illustrate a tradeoff exposed by our theoretical analysis: as we increase the portfolio size, we can hope to include a well-suited parameter setting for every possible problem instance, but it becomes impossible to avoid overfitting. 

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4. Adaptive Task-Oriented Resource Allocation for Large Dynamic Workflows on Opportunistic Resources

   https://doi.org/10.1109/IPDPS57955.2024.00034  

   Phung, Thanh Son; Thain, Douglas (May 2024, IEEE)

   Dynamic workflow management systems offer a solution to the problem of distributing a local application by packaging individual computations and their dependencies on- the-fly into tasks executable on remote workers. Such inde- pendent task execution allows workers to be launched in an opportunistic manner to maximize the current pool of resources at any given time, either through opportunistic systems (e.g., HTCondor, AWS Spot Instances), or conventional systems (e.g., SLURM, SGE) with backfilling enabled, as opposed to monolithic or message-passing applications requiring a fixed block of non- preemptible workers. However, the dynamic nature of task generation presents a significant challenge in terms of resource management as tasks must be allocated with some unknown amount of resources pre-execution but are only observable at runtime. This in turn results in potentially huge resource waste per task as (1) users lack direct knowledge about the relationship between tasks and resources, and thus cannot correctly specify the amount of resources a task needs in advance, and (2) workflows and tasks may exhibit stochastic behaviors at runtime, which complicates the process of resource management. In this paper, we (1) argue for the need of an adaptive resource allocator capable of allocating tasks at runtime and adjusting to random fluctuations and abrupt changes in a dynamic workflow without requiring any prior knowledge, and (2) introduce Greedy Bucketing and Exhaustive Bucketing: two robust, online, general- purpose, and prior-free allocation algorithms capable of producing quality estimates of a task’s resource consumption as the work- flow runs. Our results show that a resource allocator equipped with either algorithm consistently outperforms 5 alternative allocation algorithms on 7 diverse workflows and incurs at most 1.6 ms overhead per allocation in the steady state. 

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5. On Distributed Online Convex Optimization with Sublinear Dynamic Regret and Fit

   https://doi.org/10.1109/IEEECONF53345.2021.9723285  

   Sharma, Pranay; Khanduri, Prashant; Shen, Lixin; Bucci, Donald J.; Varshney, Pramod K. (January 2022, 2021 55th Asilomar Conference on Signals, Systems, and Computers)

   In this work, we consider a distributed online convex optimization problem, with time-varying (potentially adversarial) constraints. A set of nodes, jointly aim to minimize a global objective function, which is the sum of local convex functions. The objective and constraint functions are revealed locally to the nodes, at each time, after taking an action. Naturally, the constraints cannot be instantaneously satisfied. Therefore, we reformulate the problem to satisfy these constraints in the long term. To this end, we propose a distributed primal-dual mirror descent-based algorithm, in which the primal and dual updates are carried out locally at all the nodes. This is followed by sharing and mixing of the primal variables by the local nodes via communication with the immediate neighbors. To quantify the performance of the proposed algorithm, we utilize the challenging, but more realistic metrics of dynamic regret and fit. Dynamic regret measures the cumulative loss incurred by the algorithm compared to the best dynamic strategy, while fit measures the long term cumulative constraint violations. Without assuming the restrictive Slater’s conditions, we show that the proposed algorithm achieves sublinear regret and fit under mild, commonly used assumptions. 

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