Optimizing Performance of Continuous-Time Stochastic Systems using Timeout Synthesis

We consider parametric version of fixed-delay continuous-time Markov chains (or equivalently deterministic and stochastic Petri nets, DSPN) where fixed-delay transitions are specified by parameters, rather than concrete values. Our goal is to synthesize values of these parameters that, for a given cost function, minimise expected total cost incurred before reaching a given set of target states. We show that under mild assumptions, optimal values of parameters can be effectively approximated using translation to a Markov decision process (MDP) whose actions correspond to discretized values of these parameters

Extension of PRISM by Synthesis of Optimal Timeouts in Fixed-Delay CTMC

We present a practically appealing extension of the probabilistic model checker PRISM rendering it to handle fixed-delay continuous-time Markov chains (fdCTMCs) with rewards, the equivalent formalism to the deterministic and stochastic Petri nets (DSPNs). fdCTMCs allow transitions with fixed-delays (or timeouts) on top of the traditional transitions with exponential rates. Our extension supports an evaluation of expected reward until reaching a given set of target states. The main contribution is that, considering the fixed-delays as parameters, we implemented a synthesis algorithm that computes the epsilon-optimal values of the fixed-delays minimizing the expected reward. We provide a performance evaluation of the synthesis on practical examples

Mean-Payoff Optimization in Continuous-Time Markov Chains with Parametric Alarms

Continuous-time Markov chains with alarms (ACTMCs) allow for alarm events that can be non-exponentially distributed. Within parametric ACTMCs, the parameters of alarm-event distributions are not given explicitly and can be subject of parameter synthesis. An algorithm solving the $\varepsilon$-optimal parameter synthesis problem for parametric ACTMCs with long-run average optimization objectives is presented. Our approach is based on reduction of the problem to finding long-run average optimal strategies in semi-Markov decision processes (semi-MDPs) and sufficient discretization of parameter (i.e., action) space. Since the set of actions in the discretized semi-MDP can be very large, a straightforward approach based on explicit action-space construction fails to solve even simple instances of the problem. The presented algorithm uses an enhanced policy iteration on symbolic representations of the action space. The soundness of the algorithm is established for parametric ACTMCs with alarm-event distributions satisfying four mild assumptions that are shown to hold for uniform, Dirac and Weibull distributions in particular, but are satisfied for many other distributions as well. An experimental implementation shows that the symbolic technique substantially improves the efficiency of the synthesis algorithm and allows to solve instances of realistic size.Comment: This article is a full version of a paper accepted to the Conference on Quantitative Evaluation of SysTems (QEST) 201

Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded

Decision trees usefully represent sparse, high dimensional and noisy data. Having learned a function from this data, we may want to thereafter integrate the function into a larger decision-making problem, e.g., for picking the best chemical process catalyst. We study a large-scale, industrially-relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted trees and penalty functions mitigating risk. This mixed-integer optimization problem with convex penalty terms broadly applies to optimizing pre-trained regression tree models. Decision makers may wish to optimize discrete models to repurpose legacy predictive models, or they may wish to optimize a discrete model that particularly well-represents a data set. We develop several heuristic methods to find feasible solutions, and an exact, branch-and-bound algorithm leveraging structural properties of the gradient-boosted trees and penalty functions. We computationally test our methods on concrete mixture design instance and a chemical catalysis industrial instance

CTMCs with Imprecisely Timed Observations

Labeled continuous-time Markov chains (CTMCs) describe processes subject to random timing and partial observability. In applications such as runtime monitoring, we must incorporate past observations. The timing of these observations matters but may be uncertain. Thus, we consider a setting in which we are given a sequence of imprecisely timed labels called the evidence. The problem is to compute reachability probabilities, which we condition on this evidence. Our key contribution is a method that solves this problem by unfolding the CTMC states over all possible timings for the evidence. We formalize this unfolding as a Markov decision process (MDP) in which each timing for the evidence is reflected by a scheduler. This MDP has infinitely many states and actions in general, making a direct analysis infeasible. Thus, we abstract the continuous MDP into a finite interval MDP (iMDP) and develop an iterative refinement scheme to upper-bound conditional probabilities in the CTMC. We show the feasibility of our method on several numerical benchmarks and discuss key challenges to further enhance the performance

CTMCs with Imprecisely Timed Observations

Labeled continuous-time Markov chains (CTMCs) describe processes subject to random timing and partial observability. In applications such as runtime monitoring, we must incorporate past observations. The timing of these observations matters but may be uncertain. Thus, we consider a setting in which we are given a sequence of imprecisely timed labels called the evidence. The problem is to compute reachability probabilities, which we condition on this evidence. Our key contribution is a method that solves this problem by unfolding the CTMC states over all possible timings for the evidence. We formalize this unfolding as a Markov decision process (MDP) in which each timing for the evidence is reflected by a scheduler. This MDP has infinitely many states and actions in general, making a direct analysis infeasible. Thus, we abstract the continuous MDP into a finite interval MDP (iMDP) and develop an iterative refinement scheme to upper-bound conditional probabilities in the CTMC. We show the feasibility of our method on several numerical benchmarks and discuss key challenges to further enhance the performance.Comment: Extended version (with appendix) of the paper accepted at TACAS 202

CTMCs with Imprecisely Timed Observations

Labeled continuous-time Markov chains (CTMCs) describe processes subject to random timing and partial observability. In applications such as runtime monitoring, we must incorporate past observations. The timing of these observations matters but may be uncertain. Thus, we consider a setting in which we are given a sequence of imprecisely timed labels called the evidence. The problem is to compute reachability probabilities, which we condition on this evidence. Our key contribution is a method that solves this problem by unfolding the CTMC states over all possible timings for the evidence. We formalize this unfolding as a Markov decision process (MDP) in which each timing for the evidence is reflected by a scheduler. This MDP has infinitely many states and actions in general, making a direct analysis infeasible. Thus, we abstract the continuous MDP into a finite interval MDP (iMDP) and develop an iterative refinement scheme to upper-bound conditional probabilities in the CTMC. We show the feasibility of our method on several numerical benchmarks and discuss key challenges to further enhance the performance