In this paper, we present a deep learning technique-based method to solve large-scale 0-1 knapsack problems where the number of products (items) is large and/or the values of products are not necessarily predetermined but decided by an external value assignment function during the optimization process. Our solution is greatly inspired by the method of Lagrange multiplier and some recent adoptions of game theory to deep learning. After formally defining our proposed method based on them, we develop an adaptive gradient ascent method to stabilize its optimization process. In our experiments, the presented method solves all the large-scale benchmark KP instances in about a minute, whereas existing methods show fluctuating runtime. We also show that our method can be used for other applications, including but not limited to the point cloud resampling.

In the last decades we have witnessed the success of applications of Artificial Intelligence to playing games. In this work we address the challenging field of games with hidden information and card games in particular. Jass is a very popular card game in Switzerland and is closely connected with Swiss culture. To the best of our knowledge, performances of Artificial Intelligence agents in the game of Jass do not outperform top players yet. Our contribution to the community is two-fold. First, we provide an overview of the current state-of-the-art of Artificial Intelligence methods for card games in general. Second, we discuss their application to the use-case of the Swiss card game Jass. This paper aims to be an entry point for both seasoned researchers and new practitioners who want to join in the Jass challenge.

We consider the stochastic linear (multi-armed) contextual bandit problem with the possibility of hidden \textit{simple multi-armed bandit} structure in which the rewards are independent of the contextual information. Algorithms that are designed solely for one of the regimes are known to be sub-optimal for their alternate regime. We design a single computationally efficient algorithm that simultaneously obtains problem-dependent optimal regret rates in the simple multi-armed bandit regime and minimax optimal regret rates in the linear contextual bandit regime, without knowing a priori which of the two models generates the rewards. These results are proved under the condition of stochasticity of contextual information over multiple rounds. Our results should be viewed as a step towards principled data-dependent policy class selection for contextual bandits.

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can stabilize invariants characterizing these objects. We outline how so called contour functions induce relevant metrics for stabilizing the rank invariant. On the practical level, the stable ranks are used as fingerprints for data. Different choices of contour lead to different stable ranks and the topological learning is then the question of finding the optimal contour. We outline our analysis pipeline and show how it can enhance classification of physical activities data. As our main application we study how stable ranks and contours provide robust descriptors of spatial patterns of atmospheric cloud fields.

Generative adversarial networks have been very successful in generative modeling, however they remain relatively hard to optimize compared to standard deep neural networks. In this paper, we try to gain insight into the optimization of GANs by looking at the game vector field resulting from the concatenation of the gradient of both players. Based on this point of view, we propose visualization techniques that allow us to make the following empirical observations. First, the training of GANs suffers from rotational behavior around locally stable stationary points, which, as we show, corresponds to the presence of imaginary components in the eigenvalues of the Jacobian of the game. Secondly, GAN training seems to converge to a stable stationary point which is a saddle point for the generator loss, not a minimum, while still achieving excellent performance. This counter-intuitive yet persistent observation questions whether we actually need a Nash equilibrium to get good performance in GANs.

We introduce Minimal Achievable Sufficient Statistic (MASS) Learning, a training method for machine learning models that attempts to produce minimal sufficient statistics with respect to a class of functions (e.g. deep networks) being optimized over. In deriving MASS Learning, we also introduce Conserved Differential Information (CDI), an information-theoretic quantity that - unlike standard mutual information - can be usefully applied to deterministically-dependent continuous random variables like the input and output of a deep network. In a series of experiments, we show that deep networks trained with MASS Learning achieve competitive performance on supervised learning and uncertainty quantification benchmarks.

Multi-agent learning is a promising method to simulate aggregate competitive behaviour in finance. Learning expert agents' reward functions through their external demonstrations is hence particularly relevant for subsequent design of realistic agent-based simulations. Inverse Reinforcement Learning (IRL) aims at acquiring such reward functions through inference, allowing to generalize the resulting policy to states not observed in the past. This paper investigates whether IRL can infer such rewards from agents within real financial stochastic environments: limit order books (LOB). We introduce a simple one-level LOB, where the interactions of a number of stochastic agents and an expert trading agent are modelled as a Markov decision process. We consider two cases for the expert's reward: either a simple linear function of state features; or a complex, more realistic non-linear function. Given the expert agent's demonstrations, we attempt to discover their strategy by modelling their latent reward function using linear and Gaussian process (GP) regressors from previous literature, and our own approach through Bayesian neural networks (BNN). While the three methods can learn the linear case, only the GP-based and our proposed BNN methods are able to discover the non-linear reward case. Our BNN IRL algorithm outperforms the other two approaches as the number of samples increases. These results illustrate that complex behaviours, induced by non-linear reward functions amid agent-based stochastic scenarios, can be deduced through inference, encouraging the use of inverse reinforcement learning for opponent-modelling in multi-agent systems.

This paper addresses the following question of neural network identifiability: Does the input-output map realized by a feed-forward neural network with respect to a given nonlinearity uniquely specify the network architecture, weights, and biases? Existing literature on the subject Sussman 1992, Albertini, Sontag et.al 1993, Fefferman 1994 suggests that the answer should be yes, up to certain symmetries induced by the nonlinearity, and provided the networks under consideration satisfy certain "genericity conditions". The results in Sussman 1992 and Albertini, Sontag et.al 1993 apply to networks with a single hidden layer and in Fefferman 1994 the networks need to be fully connected. In an effort to answer the identifiability question in greater generality, we derive necessary genericity conditions for the identifiability of neural networks of arbitrary depth and connectivity with an arbitrary nonlinearity. Moreover, we construct a family of nonlinearities for which these genericity conditions are minimal, i.e., both necessary and sufficient. This family is large enough to approximate many commonly encountered nonlinearities to arbitrary precision in the uniform norm.

Algorithms that fuse multiple input sources benefit from both complementary and shared information. Shared information may provide robustness to faulty or noisy inputs, which is indispensable for safety-critical applications like self-driving cars. We investigate learning fusion algorithms that are robust against noise added to a single source. We first demonstrate that robustness against single source noise is not guaranteed in a linear fusion model. Motivated by this discovery, two possible approaches are proposed to increase robustness: a carefully designed loss with corresponding training algorithms for deep fusion models, and a simple convolutional fusion layer that has a structural advantage in dealing with noise. Experimental results show that both training algorithms and our fusion layer make a deep fusion-based 3D object detector robust against noise applied to a single source, while preserving the original performance on clean data.

This paper presents a two-step generative approach for creating While research on level generation focuses on level generators dungeons in the rogue-like puzzle game MiniDungeons 2. Generation based on stochastic search [14], constraint solving [11, 12], or machine is split into two steps, initially producing the architectural learning [13], level generation in published games is mostly layout of the level as its walls and floor tiles, and then furnishing it carried out via constructive algorithms. Unlike generate-and-test with game objects representing the player's start and goal position, processes, constructive generators do not evaluate and regenerate challenges and rewards. Three layout creators and three furnishers output; for example, cellular automata and grammars can be used are introduced in this paper, which can be combined in different for constructive generation, as well as more freeform approaches ways in the two-step generative process for producing diverse dungeons such as diggers [10]. Such generators are computationally lightweight levels. Layout creators generate the floors and walls of a level, since they do not evaluate their generated output. This while furnishers populate it with monsters, traps, and treasures.