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Managing Temporal Resolution in Continuous Value Estimation: A Fundamental Trade-off

Zichen (Vincent) Zhang · Johannes Kirschner · Junxi Zhang · Francesco Zanini · Alex Ayoub · Masood Dehghan · Dale Schuurmans

Great Hall & Hall B1+B2 (level 1) #1402
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[ Paper [ Poster [ OpenReview
Thu 14 Dec 8:45 a.m. PST — 10:45 a.m. PST


A default assumption in reinforcement learning (RL) and optimal control is that observations arrive at discrete time points on a fixed clock cycle. Yet, many applications involve continuous-time systems where the time discretization, in principle, can be managed. The impact of time discretization on RL methods has not been fully characterized in existing theory, but a more detailed analysis of its effect could reveal opportunities for improving data-efficiency. We address this gap by analyzing Monte-Carlo policy evaluation for LQR systems and uncover a fundamental trade-off between approximation and statistical error in value estimation. Importantly, these two errors behave differently to time discretization, leading to an optimal choice of temporal resolution for a given data budget. These findings show that managing the temporal resolution can provably improve policy evaluation efficiency in LQR systems with finite data. Empirically, we demonstrate the trade-off in numerical simulations of LQR instances and standard RL benchmarks for non-linear continuous control.

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