We introduce a multi-agent simulator for economic systems comprised of heterogeneous Households, heterogeneous Firms, Central Bank and Government agents, that could be subjected to exogenous, stochastic shocks. The interaction between agents defines the production and consumption of goods in the economy alongside the flow of money. Each agent can be designed to act according to fixed, rule-based strategies or learn their strategies using interactions with others in the simulator. We ground our simulator by choosing agent heterogeneity parameters based on economic literature, while designing their action spaces in accordance with real data in the United States. Our simulator facilitates the use of reinforcement learning strategies for the agents via an OpenAI Gym style environment definition for the economic system. We demonstrate the utility of our simulator by simulating and analyzing two hypothetical (yet interesting) economic scenarios. The first scenario investigates the impact of heterogeneous household skills on their learned preferences to work at different firms. The second scenario examines the impact of a positive production shock to one of two firms on its pricing strategy in comparison to the second firm. We aspire that our platform sets a stage for subsequent research at the intersection of artificial intelligence and economics.

We consider the problem of learning Stochastic Differential Equations of the form $dX_t = f(X_t)dt+\sigma(X_t)dW_t $ from one sample trajectory. This problem is more challenging than learning deterministic dynamical systems because one sample trajectory only provides indirect information on the unknown functions $f$, $\sigma$, and stochastic process $dW_t$ representing the drift, the diffusion, and the stochastic forcing terms, respectively. We propose a method that combines Computational Graph Completion and data adapted kernels learned via a new variant of cross validation. Our approach can be decomposed as follows: (1) Represent the time-increment map $X_t \rightarrow X_{t+dt}$ as a Computational Graph in which $f$, $\sigma$ and $dW_t$ appear as unknown functions and random variables. (2) Complete the graph (approximate unknown functions and random variables) via Maximum a Posteriori Estimation (given the data) with Gaussian Process (GP) priors on the unknown functions. (3) Learn the covariance functions (kernels) of the GP priors from data with randomized cross-validation. Numerical experiments illustrate the efficacy, robustness, and scope of our method.

Functional data analysis has long been used in modeling time series enabling long term predictions with the ability to We propose a novel group of Gaussian Process based algorithms work with irregularly sampled data [7]. In time series modeling, for fast approximate optimal stopping of time series with specific approaches based on Gaussian Processes (GPs) allow long term applications to financial markets. We show that structural properties forecasting in settings with small quantities of data for calibration commonly exhibited by financial time series (e.g., the tendency and those with a need to estimate the covariance of predictions [30, to mean-revert) allow the use of Gaussian and Deep Gaussian Process 17]. GPs also come up in finance when studying mean reverting models that further enable us to analytically evaluate optimal processes called Ornstein-Uhlenbeck (OU) processes which are GPs stopping value functions and policies. We additionally quantify with an exponential kernel [29].

K-Nearest Neighbors (KNN) search is a fundamental algorithm in artificial intelligence software with applications in robotics, and autonomous vehicles. These wide-ranging applications utilize KNN either directly for simple classification or combine KNN results as input to other algorithms such as Locally Weighted Learning (LWL). Similar to binary trees, kd-trees become unbalanced as new data is added in online applications which can lead to rapid degradation in search performance unless the tree is rebuilt. Although approximate methods are suitable for graphics applications, which prioritize query speed over query accuracy, they are unsuitable for certain applications in autonomous systems, aeronautics, and robotic manipulation where exact solutions are desired. In this paper, we will attempt to assess the performance of non-recursive deterministic kd-tree functions and KNN functions. We will also present a "forest of interval kd-trees" which reduces the number of tree rebuilds, without compromising the exactness of query results.

The design and testing of supervised machine learning models combine two fundamental distributions: (1) the training data distribution (2) the testing data distribution. Although these two distributions are identical and identifiable when the data set is infinite; they are imperfectly known (and possibly distinct) when the data is finite (and possibly corrupted) and this uncertainty must be taken into account for robust Uncertainty Quantification (UQ). We present a general decision-theoretic bootstrapping solution to this problem: (1) partition the available data into a training subset and a UQ subset (2) take $m$ subsampled subsets of the training set and train $m$ models (3) partition the UQ set into $n$ sorted subsets and take a random fraction of them to define $n$ corresponding empirical distributions $\mu_{j}$ (4) consider the adversarial game where Player I selects a model $i\in\left\{ 1,\ldots,m\right\} $, Player II selects the UQ distribution $\mu_{j}$ and Player I receives a loss defined by evaluating the model $i$ against data points sampled from $\mu_{j}$ (5) identify optimal mixed strategies (probability distributions over models and UQ distributions) for both players. These randomized optimal mixed strategies provide optimal model mixtures and UQ estimates given the adversarial uncertainty of the training and testing distributions represented by the game. The proposed approach provides (1) some degree of robustness to distributional shift in both the distribution of training data and that of the testing data (2) conditional probability distributions on the output space forming aleatory representations of the uncertainty on the output as a function of the input variable.