Breast cancer is one of the most prevalent types of cancer today in women. The main avenue of diagnosis is through manual examination of histopathology tissue slides. Such a process is often subjective and error-ridden, suffering from both inter- and intraobserver variability. Our objective is to develop an automatic algorithm for analysing histopathology slides free of human subjectivity. Here, we calculate the fractal dimension of images of numerous breast cancer slides, at magnifications of 40×, 100×, 200× and 400×. Using machine learning, specifically, the support vector machine (SVM) method, the F1 score for classification accuracy of the 40× slides was found to be 0.979. Multiclass classification on the 40× slides yielded an accuracy of 0.556. A reduction of the size and scope of the SVM training set gave an average F1 score of 0.964. Taken together, these results show great promise in the use of fractal dimension to predict tumour malignancy.
We explore fixed-horizon temporal difference (TD) methods, reinforcement learning algorithms for a new kind of value function that predicts the sum of rewards over a fixed number of future time steps. To learn the value function for horizon h, these algorithms bootstrap from the value function for horizon h−1, or some shorter horizon. Because no value function bootstraps from itself, fixed-horizon methods are immune to the stability problems that plague other off-policy TD methods using function approximation (also known as “the deadly triad”). Although fixed-horizon methods require the storage of additional value functions, this gives the agent additional predictive power, while the added complexity can be substantially reduced via parallel updates, shared weights, and n-step bootstrapping. We show how to use fixed-horizon value functions to solve reinforcement learning problems competitively with methods such as Q-learning that learn conventional value functions. We also prove convergence of fixed-horizon temporal difference methods with linear and general function approximation. Taken together, our results establish fixed-horizon TD methods as a viable new way of avoiding the stability problems of the deadly triad.
Approximate Policy Iteration (API) algorithms alternate between (approximate) policy evaluation and (approximate) greedification. Many different approaches have been explored for approximate policy evaluation, but less is understood about approximate greedification and what choices guarantee policy improvement. In this work, we investigate approximate greedification when reducing the KL divergence between the parameterized policy and the Boltzmann distribution over action values. In particular, we investigate the difference between the forward and reverse KL divergences, with varying degrees of entropy regularization. We show that the reverse KL has stronger policy improvement guarantees, but that reducing the forward KL can result in a worse policy. We also demonstrate, however, that a large enough reduction of the forward KL can induce improvement under additional assumptions. Empirically, we show on simple continuous-action environments that the forward KL can induce more exploration, but at the cost of a more suboptimal policy. No significant differences were observed in the discrete-action setting or on a suite of benchmark problems. Throughout, we highlight that many policy gradient methods can be seen as an instance of API, with either the forward or reverse KL for the policy update, and discuss next steps for understanding and improving our policy optimization algorithms.
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