Deterministic Variant Research Articles

Fair Incentives for Repeated Engagement

We study a decision-maker’s problem of finding optimal monetary incentive schemes for retention when faced with agents whose participation decisions (stochastically) depend on the incentive they receive. Our focus is on policies constrained to fulfill two fairness properties that preclude outcomes wherein different groups of agents experience different treatment on average. We formulate the problem as a high-dimensional stochastic optimization problem and study it through the use of a closely related deterministic variant. We show that the optimal static solution to this deterministic variant is asymptotically optimal for the dynamic problem under fairness constraints. Though solving for the optimal static solution gives rise to a nonconvex optimization problem, we uncover a structural property that allows us to design a tractable, fast-converging heuristic policy. Traditional schemes for retention ignore fairness constraints; indeed, the goal in these is to use differentiation to incentivize repeated engagement with the system. Our work (i) shows that even in the absence of explicit discrimination, dynamic policies may unintentionally discriminate between agents of different types by varying the type composition of the system, and (ii) presents an asymptotically optimal policy to avoid such discriminatory outcomes.

Proposed model with weighted parameters for microgrid management: Incorporating diverse load profiles, assorted tariff policies, and energy storage devices

This study presents an optimization-based model with weighted and adjustable parameters, incorporating both deterministic and stochastic variants to enable a smooth transition between control strategies for microgrid management. The motivation to conduct this study arises from an identified gap in the literature on microgrid management, especially as not many studies tackle non-scheduled loads under different energy market policies. Considering this factor, the research objective is to ascertain the technical and economic advantages that the proposed approach offers to a microgrid characterized by a load profile that undergoes significant variations based on the day of the week. A Model Predictive Control (MPC)-based control system is employed as the system manager, using key performance indicators to assess the model’s effectiveness. The control strategy, implemented at the reference signal generator level, is designed to minimize operational costs and curb the Energy Storage System (ESS) degradation. The results demonstrate that the deterministic variant of the proposed model provides a significant quantitative return for the microgrid, especially in more stable load profiles. Additionally, the deterministic variant is a method that allows elucidating a range of values for the weighted parameters of the proposed model, which will be used in the approach stochastic variant. Conversely, the stochastic variant stands out by offering more pronounced benefits to the microgrid in scenarios with abrupt load profiles. Both versions of the model under study exhibit remarkable performance compared to the benchmark models.

Flap: A Deterministic Parser with Fused Lexing

Lexers and parsers are typically defined separately and connected by a token stream. This separate definition is important for modularity and reduces the potential for parsing ambiguity. However, materializing tokens as data structures and case-switching on tokens comes with a cost.We show how tofuseseparately-defined lexers and parsers, drastically improving performance without compromising modularity or increasing ambiguity. We propose a deterministic variant of Greibach Normal Form that ensures deterministic parsing with a single token of lookahead and makes fusion strikingly simple, and prove that normalizing context free expressions into the deterministic normal form is semantics-preserving. Our staged parser combinator library, flap, provides a standard interface, but generates specialized token-free code that runs two to six times faster than ocamlyacc on a range of benchmarks.

Optimal mining cut definition and short-term open pit production scheduling under geological uncertainty

Short-term planners must define an operational schedule based on blasthole data, which might be incomplete or imperfect. As a result, there is uncertainty in the true grade of each Selective Mining Unit. This can impact the definition of mining cuts and dig-limits, and the fulfillment of long-term targets. In this work, we propose a stochastic mixed integer program to define an operational mining cut configuration and a short-term schedule under grade uncertainty. The objective of the model is to maximize revenue and minimize deviations from production targets. We test the model using real data from a copper deposit and use grade simulations for quantifying the uncertainty in blasthole data. The results show that the stochastic model achieves higher profit margins and lower deviations from production targets compared to a deterministic variant based on a single estimated scenario. At the same time, the numerical experiments show the potential impact of blasthole uncertainty in profit and compliance of short-term schedules. Therefore, the use of this stochastic formulation can help planners find optimal mining cuts and improve target fulfillment and profitability of short-term operational plans in the presence of grade uncertainty. Finally, we propose several extensions to include new sources of uncertainty.

Performance comparisons of the three data assimilation methods for improved predictability of PM2·5: Ensemble Kalman filter, ensemble square root filter, and three-dimensional variational methods

To improve the predictability of concentrations of atmospheric particulate matter, a data assimilation (DA) system using ensemble square root filter (EnSRF) has been developed for the Community Multiscale Air Quality (CMAQ) model. The EnSRF DA method is a deterministic variant of the ensemble Kalman filter (EnKF) method, which means that unlike the EnKF method, it does not add random noise to the observations. To compare the performances of the EnSRF with those of other DA methods, such as EnKF and 3DVAR (three-dimensional variational), these three methods were applied to the same CMAQ model simulations with identical experimental settings. This is the first attempt in the field of chemical DA to compare the EnKF and EnSRF methods. An identical set of surface fine particulate matter (PM2.5) were assimilated every 6 h by all the DA methods over a CMAQ domain of East Asia, during the period from 01 May to 11 June 2016. In parallel with ‘reanalysis experiments’, we also carried out ‘48 h prediction experiments’ using the optimized initial conditions produced by the three DA methods. Detailed analyses among the three DA methods were then carried out by comparing both the reanalysis and the prediction outputs with the observed surface PM2.5 over four regions (i.e., South Korea, the Beijing–Tianjin–Hebei (BTH) region, Shandong province, and Liaoning province). The comparison results revealed that the EnSRF produced the best reanalysis and prediction fields in terms of several statistical metrics. For example, when the 3DVAR, EnKF, and EnSRF methods were used, averaged normalized mean biases (NMBs) decreased by (57.6, 85.6, and 91.8) % in reanalyses and (39.7, 87.6, and 91.5) % in first-day predictions, compared to the CMAQ control experiment (i.e., without DA) over South Korea, respectively. Also, over the three Chinese regions, the EnSRF method outperformed the EnKF and 3DVAR methods.

Non-returning deterministic and nondeterministic finite automata with translucent letters

Here, we propose a variant of the nondeterministic finite automaton with translucent letters (NFAwtl), which, after reading and deleting a letter, does not return to the left end of its tape, but instead continues from the position of the letter just deleted. When the end-of-tape marker is reached, our automaton can decide whether to accept, reject, or continue, which means that it reads the remaining tape contents again from the beginning. This type of automaton, called a non-returning finite automaton with translucent letters or an nrNFAwtl, is strictly more expressive than the NFAwtl. We study the expressive capacity of this type of automaton and that of its deterministic variant, comparing them to various other types of finite automata that do not simply read their input from left to right. Also, we are interested in the closure properties of the resulting classes of languages and in the complexity of the fixed membership problem.

Complexity guarantees for an implicit smoothing-enabled method for stochastic MPECs

Mathematical programs with equilibrium constraints (MPECs) represent a class of hierarchical programs that allow for modeling problems in engineering, economics, finance, and statistics. While stochastic generalizations have been assuming increasing relevance, there is a pronounced absence of efficient first/zeroth-order schemes with non-asymptotic rate guarantees for resolving even deterministic variants of such problems. We consider a subclass of stochastic MPECs (SMPECs) where the parametrized lower-level equilibrium problem is given by a deterministic/stochastic variational inequality problem whose mapping is strongly monotone, uniformly in upper-level decisions. Under suitable assumptions, this paves the way for resolving the implicit problem with a Lipschitz continuous objective via a gradient-free zeroth-order method by leveraging a locally randomized spherical smoothing framework. Efficient algorithms for resolving the implicit problem allow for leveraging any convexity property possessed by the implicit problem, which in turn facilitates the computation of approximate global minimizers. In this setting, we present schemes for single-stage and two-stage stochastic MPECs when the upper-level problem is either convex or nonconvex in an implicit sense. (I). Single-stage SMPECs. In single-stage SMPECs, in convex regimes, our proposed inexact schemes are characterized by a complexity in upper-level projections, upper-level samples, and lower-level projections of $${\mathcal {O}}(\tfrac{1}{\epsilon ^2})$$ , $${\mathcal {O}}(\tfrac{1}{\epsilon ^2})$$ , and $${\mathcal {O}}(\tfrac{1}{\epsilon ^2}\ln (\tfrac{1}{\epsilon }))$$ , respectively. Analogous bounds for the nonconvex regime are $${\mathcal {O}}(\tfrac{1}{\epsilon })$$ , $${\mathcal {O}}(\tfrac{1}{\epsilon ^2})$$ , and $${\mathcal {O}}(\tfrac{1}{\epsilon ^3})$$ , respectively. (II). Two-stage SMPECs. In two-stage SMPECs, in convex regimes, our proposed inexact schemes have a complexity in upper-level projections, upper-level samples, and lower-level projections of $${\mathcal {O}}(\tfrac{1}{\epsilon ^2})$$ , $${\mathcal {O}}(\tfrac{1}{\epsilon ^2})$$ , and $${\mathcal {O}}(\tfrac{1}{\epsilon ^2}\ln (\tfrac{1}{\epsilon }))$$ while the corresponding bounds in the nonconvex regime are $${\mathcal {O}}(\tfrac{1}{\epsilon })$$ , $${\mathcal {O}}(\tfrac{1}{\epsilon ^2})$$ , and $${\mathcal {O}}(\tfrac{1}{\epsilon ^2}\ln (\tfrac{1}{\epsilon }))$$ , respectively. In addition, we derive statements for accelerated schemes in settings where the exact solution of the lower-level problem is available. Preliminary numerics suggest that the schemes scale with problem size, are relatively robust to modification of algorithm parameters, show distinct benefits in obtaining near-global minimizers for convex implicit problems in contrast with competing solvers, and provide solutions of similar accuracy in a fraction of the time taken by sample-average approximation (SAA).

Quasi-deterministic 5' -> 3' Watson-Crick Automata

Watson-Crick (WK) finite automata are working on a Watson-Crick tape, that is, on a DNA molecule. A double stranded DNA molecule contains two strands, each having a 5' and a 3' end, and these two strands together form the molecule with the following properties. The strands have the same length, their 5' to 3' directions are opposite, and in each position, the two strands have nucleotides that are complement of each other (by the Watson-Crick complementary relation). Consequently, WK automata have two reading heads, one for each strand. In traditional WK automata both heads read the whole input in the same physical direction, but in 5'->3' WK automata the heads start from the two extremes and read the input in opposite direction. In sensing 5'->3' WK automata, the process on the input is finished when the heads meet, and the model is capable to accept the class of linear context-free languages. Deterministic variants are weaker, the class named 2detLIN, a proper subclass of linear languages is accepted by them. Recently, another specific variants, the state-deterministic sensing 5'->3' WK automata are investigated in which the graph of the automaton has the special property that for each node of the graph, all out edges (if any) go to a sole node, i.e., for each state there is (at most) one state that can be reached by a direct transition. It was shown that this concept is somewhat orthogonal to the usual concept of determinism in case of sensing 5'->3' WK automata. In this paper a new concept, the quasi-determinism is investigated, that is in each configuration of a computation (if it is not finished yet), the next state is uniquely determined although the next configuration may not be, in case various transitions are enabled at the same time. We show that this new concept is a common generalisation of the usual determinism and the state-determinism, i.e., the class of quasi-deterministic sensing 5'->3' WK automata is a superclass of both of the mentioned other classes. There are various usual restrictions on WK automata, e.g., stateless or 1-limited variants. We also prove some hierarchy results among language classes accepted by various subclasses of quasi-deterministic sensing 5'->3' WK automata and also some other already known language classes.

Non-Returning Finite Automata With Translucent Letters

Here we propose a variant of the nondeterministic finite automaton with translucent letters (NFAwtl) which, after reading and deleting a letter, does not return to the left end of its tape, but rather continues from the position of the letter just deleted. When the end-of-tape marker is reached, our automaton can decide whether to accept, to reject, or to continue, which means that it again reads the remaining tape contents from the beginning. This type of automaton, called a non-returning finite automaton with translucent letters or an nrNFAwtl, is strictly more expressive than the NFAwtl. We study the expressive capacity of this type of automaton and that of its deterministic variant. Also we are interested in closure properties of the resulting classes of languages and in decision problems.

Analysis of Stochastic Bifurcations in the Eco-Epidemiological Oscillatory Model with Weak Allee Effect

An eco-epidemiological model of dynamical interaction of susceptible prey, infected prey, and predator is studied in the presence of the Allee effect and random disturbances. A bifurcation analysis of the deterministic variant of the model versus Allee parameter is carried out. Various regimes of tri-rhythmicity with coexistence of three cycles, or two cycles and one chaotic attractor are revealed. The complication of population dynamics due to stochastic transitions between coexisting oscillatory attractors and order-chaos transformations is studied both numerically and analytically, by the method of confidence ellipsoids and tori. The phenomenon of noise-induced extinction of predator with increasing amplitudes of oscillations for susceptible or infected prey is discussed.

Computational and Descriptional Power of Nondeterministic Iterated Uniform Finite-State Transducers*

An iterated uniform finite-state transducer (IUFST) runs the same length-preserving transduction, starting with a sweep on the input string and then iteratively sweeping on the output of the previous sweep. The IUFST accepts the input string by halting in an accepting state at the end of a sweep. We consider both the deterministic (IUFST) and nondeterministic (NIUFST) version of this device. We show that constant sweep bounded IUFSTs and NIUFSTs accept all and only regular languages. We study the state complexity of removing nondeterminism as well as sweeps on constant sweep bounded NIUFSTs, the descriptional power of constant sweep bounded IUFSTs and NIUFSTs with respect to classical models of finite-state automata, and the computational complexity of several decidability questions. Then, we focus on non-constant sweep bounded devices, proving the existence of a proper infinite nonregular language hierarchy depending on the sweep complexity both in the deterministic and nondeterministic case. Though NIUFSTs are “one-way” devices we show that they characterize the class of context-sensitive languages, that is, the complexity class DSpace(lin). Finally, we show that the nondeterministic devices are more powerful than their deterministic variant for a sublinear number of sweeps that is at least logarithmic.

Multi-Agent Natural Actor-Critic Reinforcement Learning Algorithms

Multi-agent actor-critic algorithms are an important part of the Reinforcement Learning (RL) paradigm. We propose three fully decentralized multi-agent natural actor-critic (MAN) algorithms in this work. The objective is to collectively find a joint policy that maximizes the average long-term return of these agents. In the absence of a central controller and to preserve privacy, agents communicate some information to their neighbors via a time-varying communication network. We prove convergence of all the three MAN algorithms to a globally asymptotically stable set of the ODE corresponding to actor update; these use linear function approximations. We show that the Kullback–Leibler divergence between policies of successive iterates is proportional to the objective function’s gradient. We observe that the minimum singular value of the Fisher information matrix is well within the reciprocal of the policy parameter dimension. Using this, we theoretically show that the optimal value of the deterministic variant of the MAN algorithm at each iterate dominates that of the standard gradient-based multi-agent actor-critic (MAAC) algorithm. To our knowledge, it is the first such result in multi-agent reinforcement learning (MARL). To illustrate the usefulness of our proposed algorithms, we implement them on a bi-lane traffic network to reduce the average network congestion. We observe an almost 25% reduction in the average congestion in 2 MAN algorithms; the average congestion in another MAN algorithm is on par with the MAAC algorithm. We also consider a generic 15 agent MARL; the performance of the MAN algorithms is again as good as the MAAC algorithm.

Solving Chance-Constrained Optimization Under Nonparametric Uncertainty Through Hilbert Space Embedding

In this article, we present an efficient algorithm for solving a class of chance-constrained optimization under nonparametric uncertainty. Our algorithm is built on the possibility of representing arbitrary distributions as functions in Reproducing Kernel Hilbert Space (RKHS). We use this foundation to formulate chance-constrained optimization as one of minimizing the distance between a desired distribution and the distribution of the constraint functions in the RKHS. We provide a systematic way of constructing the desired distribution based on the notion of scenario approximation. Furthermore, we use the kernel trick to show that the computational complexity of our reformulated optimization problem is comparable to solving a deterministic variant of the chance-constrained optimization. We validate our formulation on two important robotic applications: 1) reactive collision avoidance of mobile robots in uncertain dynamic environments and 2) inverse-dynamics-based path-tracking of manipulators under perception uncertainty. In both these applications, the underlying chance constraints are defined over nonlinear and nonconvex functions of uncertain parameters and possibly also decision variables. We also benchmark our formulation with the existing approaches in terms of sample complexity and the achieved optimal cost highlighting significant improvements in both these metrics.

A simulation-based modified backtracking search algorithm for multi-objective stochastic flexible job shop scheduling problem with worker flexibility

The flexible shop scheduling problem (FJSSP) has been an extensively studied and applied manufacturing systems in recent years. However, research has mostly focused on addressing the FJSSP in its basic form by relaxing several practical constraints. In this work, we consider FJSSP with worker flexibility and uncertain processing times. A simheuristic approach addresses the multi-objective stochastic FJSSP with worker flexibility, minimizing the expected makespan and standard deviation of makespan. This approach integrates the Monte Carlo simulation (MCS) into the proposed multi-objective modified Backtracking Search Algorithm (MBSA) framework. MBSA employs an effective population initialization strategy, dynamic mutation and crossover operators, and a transfer criterion. MCS evaluates’ promising’ solutions generated by MBSA to guide the search process. Extensive experiments are performed considering three FJSSP benchmark data sets. At first, the best parameters for the MBSA are identified using the Taguchi method. Then, for the deterministic variant of the problem, MBSA is compared with two other metaheuristics to demonstrate its effectiveness. Finally, the stochastic variant is investigated considering two factors: variation level and the probability distribution of the processing times. Computational results statistically show a significant effect of these factors on the objectives, demonstrating the importance of selecting an appropriate probability distribution in an uncertain environment.

Exponential distribution of lifetimes for transient bursting states in coupled noisy excitable systems.

The phenomenon of transient bursting, caused by additive noise in a set of two coupled FitzHugh-Nagumo oscillators, is studied by direct numerical integration and by measurements in the analog electronic circuit. In the parameter region where the unique global attractor of the deterministic system is the state of rest, introduction of low or moderate intensity fluctuations into the voltage dynamics results in the onset of a transient bursting state: sequences of intermittent bursts (patches of spikes), followed by ultimate relaxation to the equilibrium. Like genuine deterministic bursting, this behavior has its origin in the slow-fast character of the underlying dynamics. Trajectories that in the deterministic variant would converge to the state of rest can, under the action of noise, escape the local basin of attraction of the equilibrium and experience a bursting episode, before being dynamically reinjected into the region around the equilibrium. Under frozen parameter values and fixed noise intensity, the number of bursts preceding the ultimate decay strongly varies for different realizations of the additive random signal. The average duration of the transient bursting stage, bounded for weak noise, diverges when the intensity of fluctuations is raised. For sufficiently large ensembles of realizations, the lifetimes of transient bursting states, both in simulations and in the analog circuit, obey the exponential distribution. We relate this distribution to the probability for a stochastic trajectory to temporarily escape from the local basin of attraction of the equilibrium.

Reversible parallel communicating finite automata systems

We study the concept of reversibility in connection with parallel communicating systems of finite automata (PCFA in short). We define the notion of reversibility in the case of PCFA (also covering the non-deterministic case) and discuss the relationship of the reversibility of the systems and the reversibility of its components. We show that a system can be reversible with non-reversible components, and the other way around, the reversibility of the components does not necessarily imply the reversibility of the system as a whole. We also investigate the computational power of deterministic centralized reversible PCFA. We show that these very simple types of PCFA (returning or non-returning) can recognize regular languages which cannot be accepted by reversible (deterministic) finite automata, and that they can even accept languages that are not context-free. We also separate the deterministic and non-deterministic variants in the case of systems with non-returning communication. We show that there are languages accepted by non-deterministic centralized PCFA, which cannot be recognized by any deterministic variant of the same type.

Noise-induced complex oscillatory dynamics in the Zeldovich–Semenov model of a continuous stirred tank reactor

Noise-induced variability of thermochemical processes in a continuous stirred tank reactor is studied on the basis of the Zeldovich-Semenov dynamical model. For the deterministic variant of this model, mono- and bistability parametric zones as well as local and global bifurcations are determined. Noise-induced transitions between coexisting attractors (equilibria and cycles) and stochastic excitement with spike oscillations are investigated by direct numerical simulation and the analytical approach based on the stochastic sensitivity technique. For the stochastic model, the phenomenon of coherence resonance is discovered and studied.

Energy Transition, Asset Price Fluctuations, and Dynamic Portfolio Decisions

This paper analyzes the implications of short-termism on portfolio decisions of investors, and its potential consequences on green investments. We study a dynamic portfolio choice problem that contains two assets, one asset with fluctuating returns and another asset with a constant risk-free return. Fluctuating returns can arise from fossil or from clean energy-related assets. Short-termism is seen to be driven by discount rates (exponential and hyperbolic) and the decision horizon of investors. We also explore the impact of the fluctuating assets returns on the fate of the portfolio, for both a deterministic and stochastic model variant, and in cases where innovation efforts are spent for fossil fuel or clean energy sources. Detailing dynamic portfolio decisions in such a way may allow us for better pathways to empirical tests.

Complexity of stochastic dual dynamic programming

Stochastic dual dynamic programming is a cutting plane type algorithm for multi-stage stochastic optimization originated about 30 years ago. In spite of its popularity in practice, there does not exist any analysis on the convergence rates of this method. In this paper, we first establish the number of iterations, i.e., iteration complexity, required by a basic dynamic cutting plane method for solving relatively simple multi-stage optimization problems, by introducing novel mathematical tools including the saturation of search points. We then refine these basic tools and establish the iteration complexity for both deterministic and stochastic dual dynamic programming methods for solving more general multi-stage stochastic optimization problems under the standard stage-wise independence assumption. Our results indicate that the complexity of some deterministic variants of these methods mildly increases with the number of stages $T$, in fact linearly dependent on $T$ for discounted problems. Therefore, they are efficient for strategic decision making which involves a large number of stages, but with a relatively small number of decision variables in each stage. Without explicitly discretizing the state and action spaces, these methods might also be pertinent to the related reinforcement learning and stochastic control areas.

On deterministic sensing $$5'\rightarrow 3'$$ Watson–Crick finite automata: a full hierarchy in 2detLIN

Watson–Crick (abbreviated as WK) finite automata are working on double stranded DNA molecule that is also called Watson–Crick tape. Subsequently, these automata have two reading heads, one for each strand. While in traditional WK automata both heads read the whole input in the same physical direction, in $$5'\rightarrow 3'$$ WK automata the heads start from the two extremes (say $$5'$$ end of the strands) and read the input in opposite direction. In sensing $$5'\rightarrow 3'$$ WK automata the process on the input is finished when the heads meet. Since the heads of a WK automaton may read longer strings in a transition, in previous models a so-called sensing parameter took care for the proper meeting of the heads (not allowing to read the same positions of the input in the last step). Recently a new model is investigated, which works without the sensing parameter. In this paper, the deterministic counterpart is studied and is proven to accept the language class 2detLIN defined by the deterministic variant of the earlier version. However, using some of the restricted variants, e.g, all-final automata, the classes of the accepted languages are changed showing a finer hierarchy inside the class of linear context-free languages.