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Recently, Petrik et al. demonstrated that L1Regularized Approximate LinearProgramming (RALP) could produce value functions and policies which comparedfavorably to established linear value function approximation techniques likeLSPI. RALP's success primarily stems from the ability to solve the featureselection and value function approximation steps simultaneously. RALP'sperformance guarantees become looser if sampled next states are used. For verynoisy domains, RALP requires an accurate model rather than samples, which canbe unrealistic in some practical scenarios. In this paper, we demonstrate thisweakness, and then introduce Locally Smoothed L1-Regularized Approximate LinearProgramming (LS-RALP). We demonstrate that LS-RALP mitigates inaccuraciesstemming from noise even without an accurate model. We show that, given somesmoothness assumptions, as the number of samples increases, error from noiseapproaches zero, and provide experimental examples of LS-RALP's success oncommon reinforcement learning benchmark problems.

Value Function Approximation in Noisy Environments Using Locally Smoothed Regularized Approximate Linear Programs