403 research outputs found
Approximate Dynamic Programming Finally Performs Well in the Game of Tetris
International audienceTetris is a video game that has been widely used as a benchmark for various optimization techniques including approximate dynamic programming (ADP) algorithms. A look at the literature of this game shows that while ADP algorithms that have been (almost) entirely based on approximating the value function (value function based) have performed poorly in Tetris, the methods that search directly in the space of policies by learning the policy parameters using an optimization black box, such as the cross entropy (CE) method, have achieved the best reported results. This makes us conjecture that Tetris is a game in which good policies are easier to represent, and thus, learn than their corresponding value functions. So, in order to obtain a good performance with ADP, we should use ADP algorithms that search in a policy space, instead of the more traditional ones that search in a value function space. In this paper, we put our conjecture to test by applying such an ADP algorithm, called classification-based modified policy iteration (CBMPI), to the game of Tetris. Our experimental results show that for the first time an ADP algorithm, namely CBMPI, obtains the best results reported in the literature for Tetris in both small and large boards. Although the CBMPI's results are similar to those of the CE method in the large board, CBMPI uses considerably fewer (almost 1/6) samples (calls to the generative model) than CE
Optimizing the CVaR via Sampling
Conditional Value at Risk (CVaR) is a prominent risk measure that is being
used extensively in various domains. We develop a new formula for the gradient
of the CVaR in the form of a conditional expectation. Based on this formula, we
propose a novel sampling-based estimator for the CVaR gradient, in the spirit
of the likelihood-ratio method. We analyze the bias of the estimator, and prove
the convergence of a corresponding stochastic gradient descent algorithm to a
local CVaR optimum. Our method allows to consider CVaR optimization in new
domains. As an example, we consider a reinforcement learning application, and
learn a risk-sensitive controller for the game of Tetris.Comment: To appear in AAAI 201
Approximate Dynamic Programming via a Smoothed Linear Program
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural âprojectionâ of a well-studied linear program for exact dynamic programming. Such programs restrict attention to approximations that are lower bounds to the optimal cost-to-go function. Our programâthe âsmoothed approximate linear programââis distinct from such approaches and relaxes the restriction to lower bounding approximations in an appropriate fashion while remaining computationally tractable. Doing so appears to have several advantages: First, we demonstrate bounds on the quality of approximation to the optimal cost-to-go function afforded by our approach. These bounds are, in general, no worse than those available for extant LP approaches and for specific problem instances can be shown to be arbitrarily stronger. Second, experiments with our approach on a pair of challenging problems (the game of Tetris and a queueing network control problem) show that the approach outperforms the existing LP approach (which has previously been shown to be competitive with several ADP algorithms) by a substantial margin
Online Meta-learning by Parallel Algorithm Competition
The efficiency of reinforcement learning algorithms depends critically on a
few meta-parameters that modulates the learning updates and the trade-off
between exploration and exploitation. The adaptation of the meta-parameters is
an open question in reinforcement learning, which arguably has become more of
an issue recently with the success of deep reinforcement learning in
high-dimensional state spaces. The long learning times in domains such as Atari
2600 video games makes it not feasible to perform comprehensive searches of
appropriate meta-parameter values. We propose the Online Meta-learning by
Parallel Algorithm Competition (OMPAC) method. In the OMPAC method, several
instances of a reinforcement learning algorithm are run in parallel with small
differences in the initial values of the meta-parameters. After a fixed number
of episodes, the instances are selected based on their performance in the task
at hand. Before continuing the learning, Gaussian noise is added to the
meta-parameters with a predefined probability. We validate the OMPAC method by
improving the state-of-the-art results in stochastic SZ-Tetris and in standard
Tetris with a smaller, 1010, board, by 31% and 84%, respectively, and
by improving the results for deep Sarsa() agents in three Atari 2600
games by 62% or more. The experiments also show the ability of the OMPAC method
to adapt the meta-parameters according to the learning progress in different
tasks.Comment: 15 pages, 10 figures. arXiv admin note: text overlap with
arXiv:1702.0311
How Fast Can We Play Tetris Greedily With Rectangular Pieces?
Consider a variant of Tetris played on a board of width and infinite
height, where the pieces are axis-aligned rectangles of arbitrary integer
dimensions, the pieces can only be moved before letting them drop, and a row
does not disappear once it is full. Suppose we want to follow a greedy
strategy: let each rectangle fall where it will end up the lowest given the
current state of the board. To do so, we want a data structure which can always
suggest a greedy move. In other words, we want a data structure which maintains
a set of rectangles, supports queries which return where to drop the
rectangle, and updates which insert a rectangle dropped at a certain position
and return the height of the highest point in the updated set of rectangles. We
show via a reduction to the Multiphase problem [P\u{a}tra\c{s}cu, 2010] that on
a board of width , if the OMv conjecture [Henzinger et al., 2015]
is true, then both operations cannot be supported in time
simultaneously. The reduction also implies polynomial bounds from the 3-SUM
conjecture and the APSP conjecture. On the other hand, we show that there is a
data structure supporting both operations in time on
boards of width , matching the lower bound up to a factor.Comment: Correction of typos and other minor correction
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