Degree Of Suboptimality Research Articles

CLoSER: Video caching in small-cell edge networks with local content sharing

We consider the problem of video caching in an edge network consisting of a set of small-cell base stations (SBS) that can share content among themselves over a high-capacity short-delay local network, or fetch the videos from a remote server over a long-delay connection. Even though the problem of minimizing the overall video playout delay in our framework is NP-hard, we develop CLoSER, an algorithm that can efficiently compute a solution that is close to the optimal, where the degree of sub-optimality depends on the worst case video-to-cache size ratio. In comparison with related prior work on video caching and streaming, CLoSER specifically focuses on the benefits of local sharing of the initial portion of the video content in reducing the video playout delay, and provides strong optimality guarantees with a low-complexity algorithm. We extend CLoSER to an online setting where the video popularities are not known a priori but are estimated over time through a limited amount of periodic information sharing between SBSs. With such online video popularity estimation, a distributed implementation of CLoSER requires zero explicit coordination between the SBSs and runs in O(NK+KlogK) time, where N is the number of SBSs (caches) and K the maximum number of videos. We carry out simulations using YouTube and Netflix video request traces, as well as synthesized traces with the same marginal distributions as the traces but varying degree of temporal correlations, and demonstrate that our algorithm uses the SBS caches effectively to reduce the video delivery delay and conserve the remote server’s bandwidth. We also show that it outperforms two other reference caching methods adapted to our system setting, over a wide range of remote-to-local bandwidth ratios. Further, we show how CLoSER extends to the scenario where each video may need to be cached in multiple bit-rates, as in Available Bit Rate (ABR) streaming.

A Prescriptive Machine Learning Approach to Mixed-Integer Convex Optimization

We introduce a prescriptive machine learning approach to speed up the process of solving mixed-integer convex optimization (MICO) problems. We solve multiple optimization instances and train a machine learning model in advance, which we use to solve new instances. Previous works have shown that the predictions of classification algorithms enable us to solve optimization problems much faster than commercial solvers. What distinguishes this paper from the previous work is that we use a prescriptive algorithm, Optimal Policy Trees (OPT), instead of classification algorithms. Whereas classification algorithms aim to predict the correct label and consider all other labels equally undesirable, a prescriptive approach takes into account all the available decision options and their counterfactuals. We first introduce an algorithm that is purely based on OPT and also its extension. We compare their performance with Optimal Classification Trees (OCT) on various MICO problems. Test problems include transportation optimization, portfolio optimization, facility location, and hybrid vehicle control. We also experiment on real-world instances taken from the Mixed Integer Programming Library. OPT-based methods have a significant edge on finding feasible solutions, whereas OCT-based methods have a slight edge on the degree of suboptimality. The proposed extension of the pure OPT algorithm improves on the suboptimality of the solutions the algorithm produces. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: The research was funded in part by a grant from OCP to MIT.

Analytical Maneuver Library for Remote Inspection with an Underactuated Spacecraft

This paper presents an analytical library for maneuvering of an underactuated spacecraft around a central target with application to remote inspection. Free-flying small spacecraft are an attractive option for in situ remote inspection but require maneuvering strategies that are computationally simple, such that they can be implemented on a small spacecraft computer, while still allowing for constraints like plume impingement and underactuation to be included. An analytical maneuver library provides a suboptimal solution but can be computed without the need for numerical optimization. In addition, the low fuel cost of maneuvers means that the degree of suboptimality of the analytical maneuvers is marginal. To develop the library, forced circular motion is used in order to place the spacecraft in a controllable state such that external disturbances can be rejected. From there, trajectories can be designed in order to manipulate the circular motion and accomplish maneuvers such as joining the circular motion from rest or changing the circle’s radius. Conditions under which plume impingement is guaranteed to be avoided are developed, and applications of the maneuver library to point-to-point maneuvering and landing on/docking to a rotating target are shown.

Expecting the unexpected: Goal recognition for rational and irrational agents

Contemporary cost-based goal-recognition assumes rationality: that observed behaviour is more or less optimal. Probabilistic goal recognition systems, however, explicitly depend on some degree of sub-optimality to generate probability distributions. We show that, even when an observed agent is only slightly irrational (sub-optimal), state-of-the-art systems produce counter-intuitive results (though these may only become noticeable when the agent is highly irrational). We provide a definition of rationality appropriate to situations where the ground truth is unknown, define a rationality measure (RM) that quantifies an agent's expected degree of sub-optimality, and define an innovative self-modulating probability distribution formula for goal recognition. Our formula recognises sub-optimality and adjusts its level of confidence accordingly, thereby handling irrationality—and rationality—in an intuitive, principled manner. Building on that formula, moreover, we strengthen a previously published result, showing that “single-observation” recognition in the path-planning domain achieves identical results to more computationally expensive techniques, where previously we claimed only to achieve equivalent rankings though values differed.

Network Service Embedding Across Multiple Resource Dimensions

Network Function Virtualization (NFV) poses the need for efficient embeddings of network services, usually defined in the form of service graphs, associated with resource and bandwidth demands. As the scope of NFV has been expanded in order to meet the requirements of virtualized cellular networks and emerging 5G services, the diversity of resource demands across dimensions, such as CPU, memory, and storage, increased. This requirement exacerbates the already challenging problem of network service embedding (NSE), rendering most existing NSE methods inefficient, as they commonly account for a single resource dimension ( i.e. , typically, the CPU). In this context, we investigate methods for NSE optimization across multiple resource dimensions. To this end, we study a range of multi-dimensional mapping efficiency metrics and assess their suitability for heuristic and exact NSE methods. Utilizing the most suitable and efficient metrics, we propose two heuristics and a mixed integer linear program (MILP) for optimized multi-dimensional NSE. In addition, we devise a virtual network function (VNF) bundling scheme that generates (resource-wise) balanced VNF bundles in order to augment VNF placement. Our evaluation results indicate notable resource efficiency gains of the proposed heuristics compared to a single-dimensional counterpart, as well as a minor degree of sub-optimality in relation to our proposed MILP. We further demonstrate how the bundling scheme affects the embedding efficiency, when coupled with our most efficient heuristic. Our study also uncovers interesting insights and potential implications from the utilization of multi-dimensional metrics within NSE methods.

Wide variation in the suboptimal distribution of photosynthetic capacity in relation to light across genotypes of wheat.

Suboptimal distribution of photosynthetic capacity in relation to light among leaves reduces potential whole-canopy photosynthesis. We quantified the degree of suboptimality in 160 genotypes of wheat by directly measuring photosynthetic capacity and daily irradiance in flag and penultimate leaves. Capacity per unit daily irradiance was systematically lower in flag than penultimate leaves in most genotypes, but the ratio (γ) of capacity per unit irradiance between flag and penultimate leaves varied widely across genotypes, from less than 0.5 to over 1.2. Variation in γ was most strongly associated with differences in photosynthetic capacity in penultimate leaves, rather than with flag leaf photosynthesis or canopy light penetration. Preliminary genome-wide association analysis identified nine strong marker-trait associations with this trait, which should be validated in future work in other environments and/or materials. Our modelling suggests canopy photosynthesis could be increased by up to 5 % under sunny conditions by harnessing this variation through selective breeding for increased γ.

The voice of optimization

We introduce the idea that using optimal classification trees (OCTs) and optimal classification trees with-hyperplanes (OCT-Hs), interpretable machine learning algorithms developed by Bertsimas and Dunn (Mach Learn 106(7):1039–1082, 2017), we are able to obtain insight on the strategy behind the optimal solution in continuous and mixed-integer convex optimization problem as a function of key parameters that affect the problem. In this way, optimization is not a black box anymore. Instead, we redefine optimization as a multiclass classification problem where the predictor gives insights on the logic behind the optimal solution. In other words, OCTs and OCT-Hs give optimization a voice. We show on several realistic examples that the accuracy behind our method is in the 90–100% range, while even when the predictions are not correct, the degree of suboptimality or infeasibility is very low. We compare optimal strategy predictions of OCTs and OCT-Hs and feedforward neural networks (NNs) and conclude that the performance of OCT-Hs and NNs is comparable. OCTs are somewhat weaker but often competitive. Therefore, our approach provides a novel insightful understanding of optimal strategies to solve a broad class of continuous and mixed-integer optimization problems.

Complexity minimisation of suboptimal MPC without terminal constraints

This paper generalises stability analysis of Nonlinear Model Predictive Control without terminal constraints to incorporate possible suboptimality of MPC solutions and develops a framework for minimisation of computational efforts associated with obtaining such a solution. The framework is applied to primal-dual interior-point solvers by choosing the length of the prediction horizon together with a degree of suboptimality of the solution in a way that reduces algorithmic complexity while satisfying certain stability and performance guarantees. The framework ensures an optimal choice for the prediction horizon in order to minimise computational complexity if applied to linear or convex quadratic MPC problems, and acts as a good indicator to this end in the more general case of nonlinear systems. This is illustrated in a numerical case study, where we apply the proposed framework to a nonholonomic robot.

Channel Power Optimization of WDM Systems Following Gaussian Noise Nonlinearity Model in Presence of Stimulated Raman Scattering

The impact of interchannel stimulated Raman scattering (SRS) on optimization of channel powers to maximize the minimum channel margin is examined using a discrete Gaussian noise model for the Kerr nonlinearity. The simultaneous consideration of these two nonlinear effects is found to be incompatible with the goal of a convex SNR expression that can be optimized globally. A sequence of convex optimizations is employed to obtain a locally optimal solution, along with a bound on the degree of suboptimality. Optimization results obtained are most accurate for Gaussian-distributed signals, such as probabilistically shaped high-order-modulated signals. In a dispersion-uncompensated 4000-km fiber system utilizing the full C -band with perfect per-span SRS gain compensation, power optimization yields benefits of 0.25 to 2 dB over optimal spectrally flat power allocations. In systems including both C- and L -band, an optimization method that accounts for both SRS and Kerr nonlinearity effects provides a 0.23 to 0.60 dB margin benefit over a method compensating for SRS gain alone. In a system spanning only the C -band, per-span SRS gain compensation is not critical, as the maximum benefit is a 0.14 dB gain in minimum margin for optimized power allocations. By contrast, in a system spanning both C- and L -band, per-span SRS gain compensation provides a gain of up to 1.23 dB with optimized power allocations and larger gains with suboptimal power allocations.

Base-stock policies with reservations

All intensively studied and widely applied inventory control policies satisfy demand in accordance with the First-Come-First-Served (FCFS) rule, whether this demand is in backorder or not. Interestingly, this rule is sub-optimal when the fill-rate is constrained or when the backorder cost structure includes fixed costs per backorder and costs per backorder per unit time. In this paper we study the degree of sub-optimality of the FCFS rule for inventory systems controlled by the well-known base-stock policy. As an alternative to the FCFS rule, we propose and analyze a class of generalized base-stock policies that reserve some maximum number of items in stock for future demands, even if backorders exist. Our analytic results and numerical investigations show that such alternative stock reservation policies are indeed very simple and considerably improve either the fillrate or reduce the total cost, without having much effect on the backorder level.

An Approximate Cramer–Rao Lower Bound for Multiple LFMCW Signals

In this paper we focus on deriving an approximate Cramer–Rao lower bound (CRLB) for the parameters of a multicomponent linear frequency modulated continuous wave (LFMCW) signal corrupted by complex additive white Gaussian noise. The approximation is necessary due to the discontinuities inherent in the mathematical model of the instantaneous phase of each LFMCW signal model. By comparing our approximate bound to a simulation of the maximum likelihood estimator (MLE) of the LFMCW parameters, we confirm our analysis. In general, the CRLB is a useful tool for feasibility studies or in evaluating the degree of suboptimality that non-MLE methods exhibit. For passive detection and estimation of LFMCW signals, the Generalized Likelihood Ratio Test and the associated MLE are difficult to implement in practice, primarily due to their large computational requirements. So, lower bounds on performance, such as those provided by the CRLB, are necessary to evaluate suboptimal methods that are more suited for practical implementations.

Resource-aware MPC for constrained linear systems: Two rollout approaches

In systems with resource constraints, such as actuation limitations in sparse control applications or limited bandwidth in networked control systems, it is desirable to use control signals that are either sparse or sporadically changing in time. Motivated by these applications, in this paper we propose two resource-aware MPC schemes for discrete-time linear systems subject to state and input constraints. The two MPC schemes exploit ideas from rollout strategies to determine simultaneously the new (continuous) control inputs and the (discrete) time instants at which the control actions are updated. The first scheme provides performance guarantees by design, in the sense that it allows the user to select a desired suboptimal level of performance, where the degree of suboptimality provides a trade-off between the guaranteed closed-loop control performance on the one hand and the utilization of (communication/actuation) resources on the other hand. The second scheme provides a guaranteed (average) resource utilization, while cleverly allocating these resources in order to maximize the control performance. By means of numerical examples, we demonstrate the effectiveness of the proposed strategies.

Optimal Priority Assignment to Control Tasks

In embedded real-time systems, task priorities are often assigned to meet deadlines. However, in control tasks, a late completion of a task has no catastrophic consequence; rather, it has a quantifiable impact in the control performance achieved by the task. In this article, we address the problem of determining the optimal assignment of priorities and periods of sampled-data control tasks that run over a shared computation unit. We show that the minimization of the overall cost can be performed efficiently using a branch and bound algorithm that can be further speeded up by allowing for a small degree of suboptimality. Detailed numerical simulations are presented to show the advantages of various branching alternatives, the overall algorithm effectiveness, and its scalability with the number of tasks.

Difference based estimators and infill statistics

Infill statistics, that is, statistical inference based on very dense observations over a fixed domain has become of late a subject of growing importance. On the other hand, it is a known phenomenon that in many cases infill statistics do not provide optimal rates. The degree of sub-optimality is related to how much parameter-related information is lost because of dense sampling, which in turn is related to sample path regularity. In the stationary Gaussian case this is determined by the large value behaviour of the spectral density and its derivatives. Moreover, many interesting non stationary examples such as non linear functionals of stationary Gaussian processes or diffusion processes driven by a stationary increment Gaussian process can also be seen to depend on the large value behaviour of the spectral density of the underlying process. In this article we discuss several examples in a unified frequency domain approach providing a general framework relating sample path regularity to estimation rates. This includes examples such as volatility estimation for diffusions and fractional diffusions, multifractals and non-linear functions of Gaussian processes. As a final example we include the problem of estimation in the presence of an additive white noise, known as the nugget effect or micro-structure error.

On the origins of suboptimality in human probabilistic inference.

Humans have been shown to combine noisy sensory information with previous experience (priors), in qualitative and sometimes quantitative agreement with the statistically-optimal predictions of Bayesian integration. However, when the prior distribution becomes more complex than a simple Gaussian, such as skewed or bimodal, training takes much longer and performance appears suboptimal. It is unclear whether such suboptimality arises from an imprecise internal representation of the complex prior, or from additional constraints in performing probabilistic computations on complex distributions, even when accurately represented. Here we probe the sources of suboptimality in probabilistic inference using a novel estimation task in which subjects are exposed to an explicitly provided distribution, thereby removing the need to remember the prior. Subjects had to estimate the location of a target given a noisy cue and a visual representation of the prior probability density over locations, which changed on each trial. Different classes of priors were examined (Gaussian, unimodal, bimodal). Subjects' performance was in qualitative agreement with the predictions of Bayesian Decision Theory although generally suboptimal. The degree of suboptimality was modulated by statistical features of the priors but was largely independent of the class of the prior and level of noise in the cue, suggesting that suboptimality in dealing with complex statistical features, such as bimodality, may be due to a problem of acquiring the priors rather than computing with them. We performed a factorial model comparison across a large set of Bayesian observer models to identify additional sources of noise and suboptimality. Our analysis rejects several models of stochastic behavior, including probability matching and sample-averaging strategies. Instead we show that subjects' response variability was mainly driven by a combination of a noisy estimation of the parameters of the priors, and by variability in the decision process, which we represent as a noisy or stochastic posterior.

Projection-free parallel quadratic programming for linear model predictive control

A key component in enabling the application of model predictive control (MPC) in fields such as automotive, aerospace, and factory automation is the availability of low-complexity fast optimisation algorithms to solve the MPC finite horizon optimal control problem in architectures with reduced computational capabilities. In this paper, we introduce a projection-free iterative optimisation algorithm and discuss its application to linear MPC. The algorithm, originally developed by Brand for non-negative quadratic programs, is based on a multiplicative update rule and it is shown to converge to a fixed point which is the optimum. An acceleration technique based on a projection-free line search is also introduced, to speed-up the convergence to the optimum. The algorithm is applied to MPC through the dual of the quadratic program (QP) formulated from the MPC finite time optimal control problem. We discuss how termination conditions with guaranteed degree of suboptimality can be enforced, and how the algorithm performance can be optimised by pre-computing the matrices in a parametric form. We show computational results of the algorithm in three common case studies and we compare such results with the results obtained by other available free and commercial QP solvers.

Evaluation of Effects of Priority Preferences on Optimal Resource Allocation in Pavement Management

Certain aspects of prioritization have commonly been employed in the optimum resource allocation program for pavement maintenance management. However, issues associated with incorporating priority preferences into pavement maintenance programming have not been evaluated. For example, application of priority weights to certain problem parameters will affect the optimality of the end solution with respect to the original objective. However, the degree of loss in optimality is related to the form or structure, the magnitudes, and the range of priority weights adopted. Decision makers, who adopt such an approach, are often oblivious to the degree of sub-optimality of the solutions. Therefore, this paper presents a study that examines the implications of applying priority weights, of varying magnitudes and ranges, in the pavement maintenance programming analysis in terms of optimality of the solution/strategy.

Surface heat flux estimation with the ensemble Kalman smoother: Joint estimation of state and parameters

The estimation of surface heat fluxes based on the assimilation of land surface temperature (LST) has been achieved within a variational data assimilation (VDA) framework. Variational approaches require the development of an adjoint model, which is difficult to derive and code in the presence of thresholds and discontinuities. Also, it is computationally expensive to obtain the background error covariance for the variational approaches. Moreover, the variational schemes cannot directly provide statistical information on the accuracy of their estimates. To overcome these shortcomings, we develop an alternative data assimilation (DA) procedure based on ensemble Kalman smoother (EnKS) with the state augmentation method. The unknowns of the assimilation scheme are neutral turbulent heat transfer coefficient (that scales the sum of turbulent heat fluxes) and evaporative fraction, EF (that represents partitioning among the turbulent fluxes). The new methodology is illustrated with an application to the First International Satellite Land Surface Climatology Project Field Experiment (FIFE) that includes areal average hydrometeorological forcings and flux observations. The results indicate that the EnKS model not only provides reasonably accurate estimates of EF and turbulent heat fluxes but also enables us to determine the uncertainty of estimations under various land surface hydrological conditions. The results of the EnKS model are also compared with those of an optimal smoother (a dynamic variational model). It is found that the EnKS model estimates are less than optimal. However, the degree of suboptimality is small, and its outcomes are roughly comparable to those of an optimal smoother. Overall, the results from this test indicate that EnKS is an efficient and flexible data assimilation procedure that is able to extract useful information on the partitioning of available surface energy from LST measurements and eventually provides reliable estimates of turbulent heat fluxes.

Suboptimality Analysis of Distributed Quasi-Nonlinear Model Predictive Control

Abstract A suboptimal approach to distributed NMPC for systems consisting of nonlinear subsystems with nonlinearly coupled dynamics subject to both state and input constraints is proposed. The approach applies linearization and a dynamic dual decomposition method to reformulate the original centralized NMPC problem into a distributed quasi-NMPC problem. An estimate of the degree of suboptimality of the distributed quasi-NMPC control in closed-loop with the nonlinear system is derived.

Evaluation of the Pre-Posterior Distribution of Optimized Sampling Times for the Design of Pharmacokinetic Studies

Information theoretic methods are often used to design studies that aim to learn about pharmacokinetic and linked pharmacokinetic–pharmacodynamic systems. These design techniques, such as D-optimality, provide the optimum experimental conditions. The performance of the optimum design will depend on the ability of the investigator to comply with the proposed study conditions. However, in clinical settings it is not possible to comply exactly with the optimum design and hence some degree of unplanned suboptimality occurs due to error in the execution of the study. In addition, due to the nonlinear relationship of the parameters of these models to the data, the designs are also locally dependent on an arbitrary choice of a nominal set of parameter values. A design that is robust to both study conditions and uncertainty in the nominal set of parameter values is likely to be of use clinically. We propose an adaptive design strategy to account for both execution error and uncertainty in the parameter values. In this study we investigate designs for a one-compartment first-order pharmacokinetic model. We do this in a Bayesian framework using Markov-chain Monte Carlo (MCMC) methods. We consider log-normal prior distributions on the parameters and investigate several prior distributions on the sampling times. An adaptive design was used to find the sampling window for the current sampling time conditional on the actual times of all previous samples.