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DTSTAMP:20260510T103951Z
DESCRIPTION:Gerad Seminars\n\nHybrid activity at GERAD\n\nSpeaker: Serdar Y
 üksel\, Queen's University\, Canada\n\nAbstract:\n\nPartially observed sto
 chastic control provides a general model for many applications. In this se
 minar\, we will first present a general introduction and then study regula
 rity\, optimality\, approximation\, and learning theoretic results for suc
 h problems.\n\nThe study of partially observed models has in general been 
 established via reducing the original partially observed stochastic contro
 l problem to a fully observed one with probability measure valued filter (
 or belief) states and an associated filtering equation forming a Markovian
  kernel. We will first establish regularity results for this kernel\, invo
 lving weak continuity as well as Wasserstein regularity and contraction\, 
 and present existence results for optimal solutions for both the discounte
 d cost (under weak continuity) and average cost (under Wasserstein regular
 ity and contraction) criteria.\n\nBuilding on these\, we then present appr
 oximation results via either quantized (probability-measure valued) filter
  approximations or finite sliding window approximations under filter stabi
 lity: Filter stability refers to the correction of an incorrectly initiali
 zed filter for a partially observed dynamical system with increasing measu
 rements. We present explicit conditions for controlled filter stability wh
 ich are then utilized to arrive at near-optimal finite-window control poli
 cies by viewing truncated memory as a uniform quantization of an alternati
 ve filter state reduction consisting of the prior at a past time stage and
  the following finite memory.\n\nFinally\, we establish the convergence of
  a reinforcement learning algorithm for control policies using these finit
 e approximations or finite window of past observations (by viewing the qua
 ntized filter values or finite window of measurements as ‘states’) and sho
 w near optimality of this approach under explicit conditions. While there 
 exist many experimental results\, (i) the rigorous asymptotic convergence 
 for such finite-memory Q-learning algorithms\, and (ii) the near optimalit
 y with an explicit rate of convergence (in the memory size) are new to the
  literature. As a corollary\, this analysis establishes near optimality of
  classical Q-learning for continuous state space stochastic control proble
 ms (by lifting them to partially observed models with approximating quanti
 zers viewed as measurement kernels) under weak continuity conditions. Exte
 nsions of the above for average cost criteria (for learning and robustness
 )\, and a general class of non-Markovian systems will also be presented. (
 Joint work with Ali D. Kara).\n\n \n\nLink of the event\n
DTSTART:20240528T150000Z
DTEND:20240528T160000Z
LOCATION:CA\, Salle 4488 Pavillon André-Aisenstadt\, Campus de l'Université
  de Montréal\, 2920\, chemin de la Tour
SUMMARY:Stochastic Control with Partial Information: Regularity\, Optimalit
 y\, Approximations\, and Learning
URL:https://www.mcgill.ca/cim/channels/event/stochastic-control-partial-inf
 ormation-regularity-optimality-approximations-and-learning-357442
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