Browsing by Author "LEE, Wee Sun"

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    Accelerating Point-Based POMDP Algorithms through Successive Approximations of the Optimal Reachable Space
    (2007-04-29) HSU, David; LEE, Wee Sun; RONG, Nan
    Point-based approximation algorithms have drastically im-proved the speed of POMDP planning. This paper presents a new point-based POMDP algorithm called SARSOP. Like earlier point-based algorithms, SARSOP performs value iter-ation at a set of sampled belief points; however, it focuses on sampling near the space reachable from an initial belief point under the optimal policy. Since neither the optimal policynor the optimal reachable space is known in advance, SARSOP builds successive approximations to it through sampling and pruning. In our experiments, the new algorithm solved dif-.cult POMDP problems with more than 10,000 states. Its running time is competitive with the fastest existing point-based algorithm on most problems andfasterby manytimes on some. Our approach is complementary to existing point-based algorithms and can be integrated with them to improve their performance.
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    Semi-supervised Learning in Reproducing Kernel Hilbert Spaces Using Local Invariances
    (2006-03-14T02:03:37Z) LEE, Wee Sun; ZHANG, Xinhua; TEH, Yee Whye
    We propose a framework for semi-supervised learning in reproducing kernel Hilbert spaces using local invariances that explicitly characterize the behavior of the target function around both labeled and unlabeled data instances. Such invariances include: invariance to small changes to the data instances, invariance to averaging across a small neighbourhood around data instances, and invariance to local transformations such as translation and rotation. These invariances are approximated by minimizing loss functions on derivatives and local averages of the functions. We use a regularized cost function, consisting of the sum of loss functions penalized with the squared norm of the function, and give a representer theorem showing that an optimal function can be represented as a linear combination of a finite number of basis functions. For the representer theorem to hold, the derivatives and local averages are required to be bounded linear functionals in the reproducing kernel Hilbert space. We show that this is true in the reproducing kernel Hilbert spaces defined by Gaussian and polynomial kernels.