An agent with an inaccurate model of its environment faces a difficult choice: it can ignore the errors in its model and act in the real world in whatever way it determines is optimal with respect to its model. Alternatively, it can take a more conservative stance and eschew its model in favor of optimizing its behavior solely via real-world interaction. This latter approach can be exceedingly slow to learn from experience, while the former can lead to "planner overfitting" - aspects of the agent's behavior are optimized to exploit errors in its model. This paper explores an intermediate position in which the planner seeks to avoid overfitting through a kind of regularization of the plans it considers. We present three different approaches that demonstrably mitigate planner overfitting in reinforcement-learning environments.
Kolter2009a applied regularization techniques to LSTD @cite_9 with an algorithm they called LARS-TD. In particular, they argued that, without regularization, LSTD's performance depends heavily on the number of basis functions chosen and the size of the data set collected. If the data set is too small, the technique is prone to overfitting. They showed that @math and @math regularization yield a procedure that inherits the benefits of selecting good features while making it possible to compute the fixed point. Later work by liu2012regularized built on this work with the algorithm RO-TD, an @math regularized off policy Temporal Difference Learning method. Johns2010 cast the @math regularized fixed-point computation as a linear complementarity problem, which provides stronger solution-uniqueness guarantees than those provided for LARS-TD. petrik2010feature examined the approximate linear programming (ALP) framework for finding approximated value functions in large MDPs. They showed the benefits of adding an @math regularization constraint to the ALP that increases the error bound at training time and helps fight overfitting.
@cite_9
2112264645 1597303641 86816279 2583938035
We consider the task of reinforcement learning with linear value function approximation. Temporal difference algorithms, and in particular the Least-Squares Temporal Difference (LSTD) algorithm, provide a method for learning the parameters of the value function, but when the number of features is large this algorithm can over-fit to the data and is computationally expensive. In this paper, we propose a regularization framework for the LSTD algorithm that overcomes these difficulties. In particular, we focus on the case of l1 regularization, which is robust to irrelevant features and also serves as a method for feature selection. Although the l1 regularized LSTD solution cannot be expressed as a convex optimization problem, we present an algorithm similar to the Least Angle Regression (LARS) algorithm that can efficiently compute the optimal solution. Finally, we demonstrate the performance of the algorithm experimentally. TD( ) is a popular family of algorithms for approximate policy evaluation in large MDPs. TD( ) works by incrementally updating the value function after each observed transition. It has two major drawbacks: it makes ine cient use of data, and it requires the user to manually tune a stepsize schedule for good performance. For the case of linear value function approximations and = 0, the Least-Squares TD (LSTD) algorithm of Bradtke and Barto (Bradtke and Barto, 1996) eliminates all stepsize parameters and improves data e ciency. This paper extends Bradtke and Barto's work in three signi cant ways. First, it presents a simpler derivation of the LSTD algorithm. Second, it generalizes from = 0 to arbitrary values of ; at the extreme of = 1, the resulting algorithm is shown to be a practical formulation of supervised linear regression. Third, it presents a novel, intuitive interpretation of LSTD as a model-based reinforcement learning technique. Approximate policy evaluation with linear function approximation is a commonly arising problem in reinforcement learning, usually solved using temporal difference (TD) algorithms. In this paper we introduce a new variant of linear TD learning, called incremental least-squares TD learning, or iLSTD. This method is more data efficient than conventional TD algorithms such as TD(0) and is more computationally efficient than non-incremental least-squares TD methods such as LSTD (Bradtke & Barto 1996; Boyan 1999). In particular, we show that the per-time-step complexities of iLSTD and TD(0) are O(n), where n is the number of features, whereas that of LSTD is O(n2). This difference can be decisive in modern applications of reinforcement learning where the use of a large number features has proven to be an effective solution strategy. We present empirical comparisons, using the test problem introduced by Boyan (1999), in which iLSTD converges faster than TD(0) and almost as fast as LSTD. Deep convolutional networks have achieved successful performance in data mining field. However, training large networks still remains a challenge, as the training data may be insufficient and the model can easily get overfitted. Hence the training process is usually combined with a model regularization. Typical regularizers include weight decay, Dropout, etc. In this paper, we propose a novel regularizer, named Structured Decorrelation Constraint (SDC), which is applied to the activations of the hidden layers to prevent overfitting and achieve better generalization. SDC impels the network to learn structured representations by grouping the hidden units and encouraging the units within the same group to have strong connections during the training procedure. Meanwhile, it forces the units in different groups to learn non-redundant representations by minimizing the cross-covariance between them. Compared with Dropout, SDC reduces the co-adaptions between the hidden units in an explicit way. Besides, we propose a novel approach called Reg-Conv that can help SDC to regularize the complex convolutional layers. Experiments on extensive datasets show that SDC significantly reduces overfitting and yields very meaningful improvements on classification performance (on CIFAR-10 6.22 accuracy promotion and on CIFAR-100 9.63 promotion).