We propose a novel, tractable latent state inference scheme for Markov jump processes, for which exact inference is often intractable. Our approach is based on an entropic matching framework that can be embedded into the well-known expectation propagation algorithm. We demonstrate the effectiveness of our method by providing closed-form results for a simple family of approximate distributions and apply it to the general class of chemical reaction networks, which are a crucial tool for modeling in systems biology. Moreover, we derive closed-form expressions for point estimation of the underlying parameters using an approximate expectation maximization procedure. We evaluate our method across various chemical reaction networks and compare it to multiple baseline approaches, demonstrating superior performance in approximating the mean of the posterior process. Finally, we discuss the limitations of our method and potential avenues for future improvement, highlighting its promising direction for addressing complex continuous-time Bayesian inference problems.

This work proposes a decision-making framework for partially observable systems in continuous time with discrete state and action spaces. As optimal decision-making becomes intractable for large state spaces we employ approximation methods for the filtering and the control problem that scale well with an increasing number of states. Specifically, we approximate the high-dimensional filtering distribution by projecting it onto a parametric family of distributions, and integrate it into a control heuristic based on the fully observable system to obtain a scalable policy. We demonstrate the effectiveness of our approach on several partially observed systems, including queueing systems and chemical reaction networks.

Load balancing arises as a fundamental problem, underlying the dimensioning and operation of many computing and communication systems, such as job routing in data center clusters, multipath communication, Big Data and queueing systems. In essence, the decision-making agent maps each arriving job to one of the possibly heterogeneous servers while aiming at an optimization goal such as load balancing, low average delay or low loss rate. One main difficulty in finding optimal load balancing policies here is that the agent only partially observes the impact of its decisions, e.g., through the delayed acknowledgements of the served jobs. In this paper, we provide a partially observable (PO) model that captures the load balancing decisions in parallel buffered systems under limited information of delayed acknowledgements. We present a simulation model for this PO system to find a load balancing policy in real-time using a scalable Monte Carlo tree search algorithm. We numerically show that the resulting policy outperforms other limited information load balancing strategies such as variants of Join-the-Most-Observations and has comparable performance to full information strategies like: Join-the-Shortest-Queue, Join-the-Shortest-Queue(d) and Shortest-Expected-Delay. Finally, we show that our approach can optimise the real-time parallel processing by using network data provided by Kaggle.

Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to consider continuous-time model formulations consisting of switching stochastic differential equations governed by an underlying Markov jump process. Inference in these types of models is however notoriously difficult, and tractable computational schemes are rare. In this work, we propose a novel inference algorithm utilizing a Markov Chain Monte Carlo approach. The presented Gibbs sampler allows to efficiently obtain samples from the exact continuous-time posterior processes. Our framework naturally enables Bayesian parameter estimation, and we also include an estimate for the diffusion covariance, which is oftentimes assumed fixed in stochastic differential equations models. We evaluate our framework under the modeling assumption and compare it against an existing variational inference approach.

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are naturally described in continuous time, we present a model based on a Markov jump process modulating a subordinated diffusion process. We provide the exact evolution equations for the prior and posterior marginal densities, the direct solutions of which are however computationally intractable. Therefore, we develop a new continuous-time variational inference algorithm, combining a Gaussian process approximation on the diffusion level with posterior inference for Markov jump processes. By minimizing the path-wise Kullback-Leibler divergence we obtain (i) Bayesian latent state estimates for arbitrary points on the real axis and (ii) point estimates of unknown system parameters, utilizing variational expectation maximization. We extensively evaluate our algorithm under the model assumption and for real-world examples.

Many processes, such as discrete event systems in engineering or population dynamics in biology, evolve in discrete space and continuous time. We consider the problem of optimal decision making in such discrete state and action space systems under partial observability. This places our work at the intersection of optimal filtering and optimal control. At the current state of research, a mathematical description for simultaneous decision making and filtering in continuous time with finite state and action spaces is still missing. In this paper, we give a mathematical description of a continuous-time partial observable Markov decision process (POMDP). By leveraging optimal filtering theory we derive a Hamilton-Jacobi-Bellman (HJB) type equation that characterizes the optimal solution. Using techniques from deep learning we approximately solve the resulting partial integro-differential equation. We present (i) an approach solving the decision problem offline by learning an approximation of the value function and (ii) an online algorithm which provides a solution in belief space using deep reinforcement learning. We show the applicability on a set of toy examples which pave the way for future methods providing solutions for high dimensional problems.

We analyse a data-processing system with n clients producing jobs which are processed in batches by m parallel servers; the system throughput critically depends on the batch size and a corresponding sub-additive speedup function. In practice, throughput optimization relies on numerical searches for the optimal batch size, a process that can take up to multiple days in existing commercial systems. In this paper, we model the system in terms of a closed queueing network; a standard Markovian analysis yields the optimal throughput in ωn4 time. Our main contribution is a mean-field model of the system for the regime where the system size is large. We show that the mean-field model has a unique, globally attractive stationary point which can be found in closed form and which characterizes the asymptotic throughput of the system as a function of the batch size. Using this expression we find the asymptotically optimal throughput in O(1) time. Numerical settings from a large commercial system reveal that this asymptotic optimum is accurate in practical finite regimes.

We study job assignment in large, heterogeneous resource-sharing clusters of servers with finite buffers. This load balancing problem arises naturally in today's communication and big data systems, such as Amazon Web Services, Network Service Function Chains, and Stream Processing. Arriving jobs are dispatched to a server, following a load balancing policy that optimizes a performance criterion such as job completion time. Our contribution is a randomized Cost-Based Scheduling (CBS) policy in which the job assignment is driven by general cost functions of the server queue lengths. Beyond existing schemes, such as the Join the Shortest Queue (JSQ), the power of d or the SQ(d) and the capacity-weighted JSQ, the notion of CBS yields new application-specific policies such as hybrid locally uniform JSQ. As today's data center clusters have thousands of servers, exact analysis of CBS policies is tedious. In this article, we derive a scaling limit when the number of servers grows large, facilitating a comparison of various CBS policies with respect to their transient as well as steady state behavior. A byproduct of our derivations is the relationship between the queue filling proportions and the server buffer sizes, which cannot be obtained from infinite buffer models. Finally, we provide extensive numerical evaluations and discuss several applications including multi-stage systems.

Recent advances in quality adaptation algorithms leave adaptive bitrate (ABR) streaming architectures at a cross-roads: When determining the sustainable video quality one may either rely on the information gathered at the client vantage point or on server and network assistance. The fundamental problem here is to determine how valuable either information is for the adaptation decision. This problem becomes particularly hard in future Internet settings such as Named Data Networking (NDN) where the notion of a network connection does not exist. In this paper, we provide a fresh view on ABR quality adaptation for QoE maximization, which we formalize as a decision problem under uncertainty, and for which we contribute a sparse Bayesian contextual bandit algorithm denoted CBA. This allows taking high-dimensional streaming context information, including client-measured variables and network assistance, to find online the most valuable information for the quality adaptation. Since sparse Bayesian estimation is computationally expensive, we develop a fast new inference scheme to support online video adaptation. We perform an extensive evaluation of our adaptation algorithm in the particularly challenging setting of NDN, where we use an emulation testbed to demonstrate the efficacy of CBA compared to state-of-the-art algorithms.

Many decision-making problems naturally exhibit pronounced structures inherited from the characteristics of the underlying environment. In a Markov decision process model, for example, two distinct states can have inherently related semantics or encode resembling physical state configurations. This often implies locally correlated transition dynamics among the states. In order to complete a certain task in such environments, the operating agent usually needs to execute a series of temporally and spatially correlated actions. Though there exists a variety of approaches to capture these correlations in continuous state-action domains, a principled solution for discrete environments is missing. In this work, we present a Bayesian learning framework based on Pólya-Gamma augmentation that enables an analogous reasoning in such cases. We demonstrate the framework on a number of common decision-making related problems, such as imitation learning, subgoal extraction, system identification and Bayesian reinforcement learning. By explicitly modeling the underlying correlation structures of these problems, the proposed approach yields superior predictive performance compared to correlation-agnostic models, even when trained on data sets that are an order of magnitude smaller in size.

Countless novel approaches to communication protocols, overlay networks, and distributed middleware are published every year, yet the adoption of such novel findings in the global Internet landscape progresses at a slow pace. Many of such new communication mechanisms excel (only) under specific deployment conditions, while user mobility and application usage patterns lead to dynamic operation conditions. This mismatch is one reason that makes a wide deployment of new specialized mechanisms particularly hard as observed, for example, for multipath transport protocol extensions until the emergence of multipath transmission control protocol (TCP). This paper formalizes the concept of Transitions, i.e., a method to instrumentalize adaptivity at runtime in communication systems. It allows to exchange communication mechanisms in a running system to optimize the communication quality. In the following, we describe the building blocks required to: 1) capture the features and relations within a communication system and 2) express and optimize the decision making process in such a system. We show how this concept maps intuitively to the Internet model which makes a protocol-independent deployment of applications feasible in the future Internet.

Collaborative uploading describes a type of crowd-sourcing scenario in networked environments where a device utilizes multiple paths over neighboring devices to upload content to a centralized processing entity such as a cloud service. Intermediate devices may aggregate and preprocess this data stream. Such scenarios arise in the composition and aggregation of information, e.g., from smart phones or sensors. We use a queuing theoretic description of the collaborative uploading scenario, capturing the ability to split data into chunks that are then transmitted over multiple paths, and finally merged at the destination. We analyze replication and allocation strategies that control the mapping of data to paths and provide closed-form expressions that pinpoint the optimal strategy given a description of the paths' service distributions. Finally, we provide an online path-aware adaptation of the allocation strategy that uses statistical inference to sequentially minimize the expected waiting time for the uploaded data. Numerical results show the effectiveness of the adaptive approach compared to the proportional allocation and a variant of the join-the-shortest-queue allocation, especially for bursty path conditions.