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publications
LP Based Bounds for Cesaro and Abel Limits of the Optimal Values in Non-ergodic Stochastic Systems
Published in 2021 European Control Conference (ECC), 2021
This paper concerns the LP formulation of non-ergodic MDPs with time averaging and time discounting criteria.
Recommended citation: Konstantin Avrachenkov, Vladimir Gaitsgory, Lucas Gamertsfelder. (2021). "LP Based Bounds for Cesaro and Abel Limits of the Optimal Values in Non-ergodic Stochastic Systems." 2021 European Control Conference (ECC). 1(3).
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LP based upper and lower bounds for Cesaro and Abel limits of the optimal values in problems of control of stochastic discrete time systems
Published in Journal of Mathematical Analysis and Applications, 2022
This paper concerns the LP formulation of non-ergodic MDPs with time averaging and time discounting criteria.
Recommended citation: Konstantin Avrachenkov, Vladimir Gaitsgory, Lucas Gamertsfelder. (2022). "LP based upper and lower bounds for Cesaro and Abel limits of the optimal values in problems of control of stochastic discrete time systems." Journal of Mathematical Analysis and Applications. 512(1).
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On convergence of occupational measures sets of a discrete-time stochastic control system, with applications to averaging of hybrid systems
Published in International Journal of Control, 2024
This paper establishes convergence of sets of random occupational measures for discrete-time stochastic systems. It then applies it to the averaging of hybrid systems.
Recommended citation: Lucas Gamertsfelder. (2024). "On convergence of occupational measures sets of a discrete-time stochastic control system, with applications to averaging of hybrid systems." International Journal of Control.
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The Effective Generalized Moment Problem
Published in ArXiv, 2025
This paper establishes polynomial convergence rates for the generalized moment problem in both the optima and feasibility sets.
Recommended citation: Lucas Gamertsfelder, Bernard Mourrain. (2024). "The Effective Generalized Moment Problem." ArXiv.
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talks
LP Based Bounds for Cesaro and Abel Limits of the Optimal Values in Non-Ergodic Stochastic Systems
Published:
In this talk, we discussed asymptotic properties of problems of control of stochastic discrete time systems (also known as Markov decision processes) with time averaging and time discounting optimality criteria. It demonstrated recent results that the Cesaro and Abel limits of the optimal values in such problems can be evaluated with the help of a certain infinite-dimensional linear programming problem and its dual. See the corresponding article here.
LP Based Bounds for Cesaro and Abel Limits of the Optimal Values in Non-Ergodic Stochastic Systems
Published:
In this talk, we discussed asymptotic properties of problems of control of stochastic discrete time systems (also known as Markov decision processes) with time averaging and time discounting optimality criteria. It demonstrated recent results that the Cesaro and Abel limits of the optimal values in such problems can be evaluated with the help of a certain infinite-dimensional linear programming problem and its dual. See the corresponding article here.
Convergence of occupational measures sets of discrete-time stochastic control systems, with applications to averaging of hybrid systems
Published:
This talk concerned recent results showing that the set of random occupational measures generated by the state-control trajectories of a discrete-time stochastic system as well as the set of their mathematical expectations converge to a non-random, convex and compact set. We apply these results to the averaging a hybrid system with a slow continuous-time component and a fast discrete-time component. It is shown that the solutions of the hybrid system are approximated by the solutions of a differential inclusion. The novelty of our results is that we allow the state-control space of the fast component to be non-denumerable. See the corresponding article here.
Moment-SoS relaxations of the generalized moment problem and applications
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This talk described an upcoming work on the application of moment-SOS hierarchies to the generalized moment problem. In particular, we recover the convergence rates of the hierarchies of relaxations in both the optima and the feasibility sets. Applications in minimal symmetric tensor decomposition and long-run optimal control were presented.
teaching
Teaching Experience 1
Undergraduate courses, Macquarie University, Department of Mathematics and Statistics, 2019
- Discrete Mathematics - DMTH137
- Mathematics IA - MATH132
- Mathematics IB - MATH133
- Mathematics IIA - MATH235
- Mathematics IIB - MATH236