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1. A General Statistical Physics Framework for Assignment Problems

   https://doi.org/10.3390/a17050212  

   Koehl, Patrice; Orland, Henri (May 2024, Algorithms)

   Linear assignment problems hold a pivotal role in combinatorial optimization, offering a broad spectrum of applications within the field of data sciences. They consist of assigning “agents” to “tasks” in a way that leads to a minimum total cost associated with the assignment. The assignment is balanced when the number of agents equals the number of tasks, with a one-to-one correspondence between agents and tasks, and it is and unbalanced otherwise. Additional options and constraints may be imposed, such as allowing agents to perform multiple tasks or allowing tasks to be performed by multiple agents. In this paper, we propose a novel framework that can solve all these assignment problems employing methodologies derived from the field of statistical physics. We describe this formalism in detail and validate all its assertions. A major part of this framework is the definition of a concave effective free energy function that encapsulates the constraints of the assignment problem within a finite temperature context. We demonstrate that this free energy monotonically decreases as a function of a parameter β representing the inverse of temperature. As β increases, the free energy converges to the optimal assignment cost. Furthermore, we demonstrate that when β values are sufficiently large, the exact solution to the assignment problem can be derived by rounding off the elements of the computed assignment matrix to the nearest integer. We describe a computer implementation of our framework and illustrate its application to multi-task assignment problems for which the Hungarian algorithm is not applicable. 

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2. Optimal soft real-time semi-partitioned scheduling made simple (and dynamic)

   https://doi.org/10.1145/3356401.3356402  

   Hobbs, Clara; Tong, Zelin; Anderson, James H. (November 2019, Proceedings of the 27th International Conference on Real-Time Networks and Systems)

   Semi-partitioned scheduling is an approach to multiprocessor real-time scheduling where most tasks are fixed to processors, while a small subset of tasks is allowed to migrate. This approach offers reduced overhead compared to global scheduling, and can reduce processor capacity loss compared to partitioned scheduling. Prior work has resulted in a number of semi-partitioned scheduling algorithms, but their correctness typically hinges on a complex intertwining of offline task assignment and online execution. This brittleness has resulted in few proposed semi-partitioned scheduling algorithms that support dynamic task systems, where tasks may join or leave the system at runtime, and few that are optimal in any sense. This paper introduces EDF-sc, the first semi-partitioned scheduling algorithm that is optimal for scheduling (static) soft real-time (SRT) sporadic task systems and allows tasks to dynamically join and leave. The SRT notion of optimality provided by EDF-sc requires deadline tardiness to be bounded for any task system that does not cause over-utilization. In the event that all tasks can be assigned as fixed, EDF-sc behaves exactly as partitioned EDF. Heuristics are provided that give EDF-sc the novel ability to stabilize the workload to approach the partitioned case as tasks join and leave the system. 

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3. Self-Stabilizing Task Allocation in Spite of Noise

   https://doi.org/10.1145/3350755.3400226  

   Dornhaus, A.R.; Lynch, N.A; Mallmann-Trenn, F.; Pajak, D.; Radeva, T. (January 2020, 32nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA))

   We study the problem of distributed task allocation by workers in an ant colony in a setting of limited capabilities and noisy environment feedback. We assume that each task has a demand that should be satisfied but not exceeded, i.e., there is an optimal number of ants that should be working on this task at a given time. The goal is to assign a near-optimal number of workers to each task in a distributed manner without explicit access to the value of the demand nor to the number of ants working on the task. We seek to answer the question of how the quality of task allocation depends on the accuracy of assessing by the ants whether too many (overload) or not enough (lack) ants are currently working on a given task. In our model, each ant receives a binary feedback that depends on the deficit, defined as the difference between the demand and the current number of workers in the task. The feedback is modeled as a random variable that takes values lack or overload with probability given by a sigmoid function of the deficit. The higher the overload or lack of workers for a task, the more likely it is that an ant receives the correct feedback from this task; the closer the deficit is to zero, the less reliable the feedback becomes. Each ant receives the feedback independently about one chosen task. We measure the performance of task allocation algorithms using the notion of inaccuracy, defined as the number of steps in which the deficit of some task is beyond certain threshold. We propose a simple, constant-memory, self-stabilizing, distributed algorithm that converges from any initial assignment to a near-optimal assignment under noisy feedback and keeps the deficit small for all tasks in almost every step. We also prove a lower bound for any constant-memory algorithm, which matches, up to a constant factor, the accuracy achieved by our algorithm. 

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4. Compositional planning in Markov decision processes: Temporal abstraction meets generalized logic composition

   Liu, Xuan; Fu, Jie (July 2019, Annual American Control Conference)

   In hierarchical planning for Markov decision processes (MDPs), temporal abstraction allows planning with macro-actions that take place at different time scale in the form of sequential composition. In this paper, we propose a novel approach to compositional reasoning and hierarchical planning for MDPs under co-safe temporal logic constraints. In addition to sequential composition, we introduce a composition of policies based on generalized logic composition: Given sub-policies for sub-tasks and a new task expressed as logic compositions of subtasks, a semi-optimal policy, which is optimal in planning with only sub-policies, can be obtained by simply composing sub-polices. Thus, a synthesis algorithm is developed to compute optimal policies efficiently by planning with primitive actions, policies for sub-tasks, and the compositions of sub-policies, for maximizing the probability of satisfying constraints specified in the fragment of co-safe temporal logic. We demonstrate the correctness and efficiency of the proposed method in stochastic planning examples with a single agent and multiple task specifications. 

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5. Self-supervised Regularization for Text Classification

   https://doi.org/10.1162/tacl_a_00389  

   Zhou, Meng; Li, Zechen; Xie, Pengtao (January 2021, Transactions of the Association for Computational Linguistics)

   Abstract Text classification is a widely studied problem and has broad applications. In many real-world problems, the number of texts for training classification models is limited, which renders these models prone to overfitting. To address this problem, we propose SSL-Reg, a data-dependent regularization approach based on self-supervised learning (SSL). SSL (Devlin et al., 2019a) is an unsupervised learning approach that defines auxiliary tasks on input data without using any human-provided labels and learns data representations by solving these auxiliary tasks. In SSL-Reg, a supervised classification task and an unsupervised SSL task are performed simultaneously. The SSL task is unsupervised, which is defined purely on input texts without using any human- provided labels. Training a model using an SSL task can prevent the model from being overfitted to a limited number of class labels in the classification task. Experiments on 17 text classification datasets demonstrate the effectiveness of our proposed method. Code is available at https://github.com/UCSD-AI4H/SSReg. 

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