8,980 research outputs found
Solving Games with Functional Regret Estimation
We propose a novel online learning method for minimizing regret in large
extensive-form games. The approach learns a function approximator online to
estimate the regret for choosing a particular action. A no-regret algorithm
uses these estimates in place of the true regrets to define a sequence of
policies.
We prove the approach sound by providing a bound relating the quality of the
function approximation and regret of the algorithm. A corollary being that the
method is guaranteed to converge to a Nash equilibrium in self-play so long as
the regrets are ultimately realizable by the function approximator. Our
technique can be understood as a principled generalization of existing work on
abstraction in large games; in our work, both the abstraction as well as the
equilibrium are learned during self-play. We demonstrate empirically the method
achieves higher quality strategies than state-of-the-art abstraction techniques
given the same resources.Comment: AAAI Conference on Artificial Intelligence 201
Discovering Valuable Items from Massive Data
Suppose there is a large collection of items, each with an associated cost
and an inherent utility that is revealed only once we commit to selecting it.
Given a budget on the cumulative cost of the selected items, how can we pick a
subset of maximal value? This task generalizes several important problems such
as multi-arm bandits, active search and the knapsack problem. We present an
algorithm, GP-Select, which utilizes prior knowledge about similarity be- tween
items, expressed as a kernel function. GP-Select uses Gaussian process
prediction to balance exploration (estimating the unknown value of items) and
exploitation (selecting items of high value). We extend GP-Select to be able to
discover sets that simultaneously have high utility and are diverse. Our
preference for diversity can be specified as an arbitrary monotone submodular
function that quantifies the diminishing returns obtained when selecting
similar items. Furthermore, we exploit the structure of the model updates to
achieve an order of magnitude (up to 40X) speedup in our experiments without
resorting to approximations. We provide strong guarantees on the performance of
GP-Select and apply it to three real-world case studies of industrial
relevance: (1) Refreshing a repository of prices in a Global Distribution
System for the travel industry, (2) Identifying diverse, binding-affine
peptides in a vaccine de- sign task and (3) Maximizing clicks in a web-scale
recommender system by recommending items to users
Bandit Algorithms for Tree Search
Bandit based methods for tree search have recently gained popularity when
applied to huge trees, e.g. in the game of go (Gelly et al., 2006). The UCT
algorithm (Kocsis and Szepesvari, 2006), a tree search method based on Upper
Confidence Bounds (UCB) (Auer et al., 2002), is believed to adapt locally to
the effective smoothness of the tree. However, we show that UCT is too
``optimistic'' in some cases, leading to a regret O(exp(exp(D))) where D is the
depth of the tree. We propose alternative bandit algorithms for tree search.
First, a modification of UCT using a confidence sequence that scales
exponentially with the horizon depth is proven to have a regret O(2^D
\sqrt{n}), but does not adapt to possible smoothness in the tree. We then
analyze Flat-UCB performed on the leaves and provide a finite regret bound with
high probability. Then, we introduce a UCB-based Bandit Algorithm for Smooth
Trees which takes into account actual smoothness of the rewards for performing
efficient ``cuts'' of sub-optimal branches with high confidence. Finally, we
present an incremental tree search version which applies when the full tree is
too big (possibly infinite) to be entirely represented and show that with high
probability, essentially only the optimal branches is indefinitely developed.
We illustrate these methods on a global optimization problem of a Lipschitz
function, given noisy data
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