A reinforcement learning agent that needs to pursue different goals across episodes requires a goal-conditional policy. In addition to their potential to generalize desirable behavior to unseen goals, such policies may also enable higher-level planning based on subgoals. In sparse-reward environments, the capacity to exploit information about the degree to which an arbitrary goal has been achieved while another goal was intended appears crucial to enable sample efficient learning. However, reinforcement learning agents have only recently been endowed with such capacity for hindsight. In this paper, we demonstrate how hindsight can be introduced to policy gradient methods, generalizing this idea to a broad class of successful algorithms. Our experiments on a diverse selection of sparse-reward environments show that hindsight leads to a remarkable increase in sample efficiency.

Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare distributions by the distance between their embeddings. We show that Regularized Maximum Mean Discrepancy (RMMD), our novel measure for kernel-based hypothesis testing, yields substantial improvements even when sample sizes are small, and excels at hypothesis tests involving multiple comparisons with power control. We derive asymptotic distributions under the null and alternative hypotheses, and assess power control. Outstanding results are obtained on: challenging EEG data, MNIST, the Berkley Covertype, and the Flare-Solar dataset.

Neuroevolution has yet to scale up to complex reinforcement learning tasks that require large networks. Networks with many inputs (e.g. raw video) imply a very high dimensional search space if encoded directly. Indirect methods use a more compact genotype representation that is transformed into networks of potentially arbitrary size. In this paper, we present an indirect method where networks are encoded by a set of Fourier coefficients which are transformed into network weight matrices via an inverse Fourier-type transform. Because there often exist network solutions whose weight matrices contain regularity (i.e. adjacent weights are correlated), the number of coefficients required to represent these networks in the frequency domain is much smaller than the number of weights (in the same way that natural images can be compressed by ignore high-frequency components). This "compressed" encoding is compared to the direct approach where search is conducted in the weight space on the high-dimensional octopus arm task. The results show that representing networks in the frequency domain can reduce the search-space dimensionality by as much as two orders of magnitude, both accelerating convergence and yielding more general solutions.

Efficient Natural Evolution Strategies (eNES) is a novel alternative to conventional evolutionary algorithms, using the natural gradient to adapt the mutation distribution. Unlike previous methods based on natural gradients, eNES uses a fast algorithm to calculate the inverse of the exact Fisher information matrix, thus increasing both robustness and performance of its evolution gradient estimation, even in higher dimensions. Additional novel aspects of eNES include optimal fitness baselines and importance mixing (a procedure for updating the population with very few fitness evaluations). The algorithm yields competitive results on both unimodal and multimodal benchmarks.

We analyze the size of the dictionary constructed from online kernel sparsification, using a novel formula that expresses the expected determinant of the kernel Gram matrix in terms of the eigenvalues of the covariance operator. Using this formula, we are able to connect the cardinality of the dictionary with the eigen-decay of the covariance operator. In particular, we show that under certain technical conditions, the size of the dictionary will always grow sub-linearly in the number of data points, and, as a consequence, the kernel linear regressor constructed from the resulting dictionary is consistent.

Traditional methods of computer vision and machine learning cannot match human performance on tasks such as the recognition of handwritten digits or traffic signs. Our biologically plausible deep artificial neural network architectures can. Small (often minimal) receptive fields of convolutional winner-take-all neurons yield large network depth, resulting in roughly as many sparsely connected neural layers as found in mammals between retina and visual cortex. Only winner neurons are trained. Several deep neural columns become experts on inputs preprocessed in different ways; their predictions are averaged. Graphics cards allow for fast training. On the very competitive MNIST handwriting benchmark, our method is the first to achieve near-human performance. On a traffic sign recognition benchmark it outperforms humans by a factor of two. We also improve the state-of-the-art on a plethora of common image classification benchmarks.

Slow Feature Analysis (SFA) extracts features representing the underlying causes of changes within a temporally coherent high-dimensional raw sensory input signal. Our novel incremental version of SFA (IncSFA) combines incremental Principal Components Analysis and Minor Components Analysis. Unlike standard batch-based SFA, IncSFA adapts along with non-stationary environments, is amenable to episodic training, is not corrupted by outliers, and is covariance-free. These properties make IncSFA a generally useful unsupervised preprocessor for autonomous learning agents and robots. In IncSFA, the CCIPCA and MCA updates take the form of Hebbian and anti-Hebbian updating, extending the biological plausibility of SFA. In both single node and deep network versions, IncSFA learns to encode its input streams (such as high-dimensional video) by informative slow features representing meaningful abstract environmental properties. It can handle cases where batch SFA fails.

Consider an embedded agent with a self-modifying, Turing-equivalent policy that can change only through active self-modifications. How can we make sure that it learns to continually accelerate reward intake? Throughout its life the agent remains ready to undo any self-modification generated during any earlier point of its life, provided the reward per time since then has not increased, thus enforcing a lifelong success-story of self-modifications, each followed by long-term reward acceleration up to the present time. The stack-based method for enforcing this is called the success-story algorithm. It fully takes into account that early self-modifications set the stage for later ones (learning a learning algorithm), and automatically learns to extend self-evaluations until the collected reward statistics are reliable ... a very simple but general method waiting to be re-discovered! Time permitting, I will also briefly discuss more recent mathematically optimal universal maximizers of lifelong reward, in particular, the fully self-referential Goedel machine.

We present a novel Natural Evolution Strategy (NES) variant, the Rank-One NES (R1-NES), which uses a low rank approximation of the search distribution covariance matrix. The algorithm allows computation of the natural gradient with cost linear in the dimensionality of the parameter space, and excels in solving high-dimensional non-separable problems, including the best result to date on the Rosenbrock function (512 dimensions).

To maximize its success, an AGI typically needs to explore its initially unknown world. Is there an optimal way of doing so? Here we derive an affirmative answer for a broad class of environments.