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We consider parametric estimation for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main targets are the drift parameter $\alpha$ and the diffusion parameter $\beta$. In this paper, we propose two types of adaptive estimators for $(\alpha,\beta)$ and show their asymptotic properties under $\varepsilon\to0$, $n\to\infty$ and the balance condition that $(\varepsilon n^\rho)^{-1} =O(1)$ for some $\rho\ge 1/2$. In simulation studies, we examine and compare asymptotic behaviors of the two kinds of adaptive estimators. Moreover, we treat the SIR model which describes a simple epidemic spread for a biological application.

Inverse probability of treatment weighting (IPTW) is a popular method for estimating the average treatment effect (ATE). However, empirical studies show that the IPTW estimators can be sensitive to the misspecification of the propensity score model. To address this problem, researchers have proposed to estimate propensity score by directly optimizing the balance of pre-treatment covariates. While these methods appear to empirically perform well, little is known about how the choice of balancing conditions affects their theoretical properties. To fill this gap, we first characterize the asymptotic bias and efficiency of the IPTW estimator based on the Covariate Balancing Propensity Score (CBPS) methodology under local model misspecification. Based on this analysis, we show how to optimally choose the covariate balancing functions and propose an optimal CBPS-based IPTW estimator. This estimator is doubly robust; it is consistent for the ATE if either the propensity score model or the outcome model is correct. In addition, the proposed estimator is locally semiparametric efficient when both models are correctly specified. To further relax the parametric assumptions, we extend our method by using a sieve estimation approach. We show that the resulting estimator is globally efficient under a set of much weaker assumptions and has a smaller asymptotic bias than the existing estimators. Finally, we evaluate the finite sample performance of the proposed estimators via simulation and empirical studies. An open-source software package is available for implementing the proposed methods.

Efficient methods to evaluate new algorithms are critical for improving interactive bandit and reinforcement learning systems such as recommendation systems. A/B tests are reliable, but are time- and money-consuming, and entail a risk of failure. In this paper, we develop an alternative method, which predicts the performance of algorithms given historical data that may have been generated by a different algorithm. Our estimator has the property that its prediction converges in probability to the true performance of a counterfactual algorithm at a rate of $\sqrt{N}$, as the sample size $N$ increases. We also show a correct way to estimate the variance of our prediction, thus allowing the analyst to quantify the uncertainty in the prediction. These properties hold even when the analyst does not know which among a large number of potentially important state variables are actually important. We validate our method by a simulation experiment about reinforcement learning. We finally apply it to improve advertisement design by a major advertisement company. We find that our method produces smaller mean squared errors than state-of-the-art methods.

Recent development of Deep Reinforcement Learning has demonstrated superior performance of neural networks in solving challenging problems with large or even continuous state spaces. One specific approach is to deploy neural networks to approximate value functions by minimising the Mean Squared Bellman Error function. Despite great successes of Deep Reinforcement Learning, development of reliable and efficient numerical algorithms to minimise the Bellman Error is still of great scientific interest and practical demand. Such a challenge is partially due to the underlying optimisation problem being highly non-convex or using incorrect gradient information as done in Semi-Gradient algorithms. In this work, we analyse the Mean Squared Bellman Error from a smooth optimisation perspective combined with a Residual Gradient formulation. Our contribution is two-fold. First, we analyse critical points of the error function and provide technical insights on the optimisation procure and design choices for neural networks. When the existence of global minima is assumed and the objective fulfils certain conditions we can eliminate suboptimal local minima when using over-parametrised neural networks. We can construct an efficient Approximate Newton's algorithm based on our analysis and confirm theoretical properties of this algorithm such as being locally quadratically convergent to a global minimum numerically. Second, we demonstrate feasibility and generalisation capabilities of the proposed algorithm empirically using continuous control problems and provide a numerical verification of our critical point analysis. We outline the short coming of Semi-Gradients. To benefit from an approximate Newton's algorithm complete derivatives of the Mean Squared Bellman error must be considered during training.

3D human pose estimation from monocular images is a highly ill-posed problem due to depth ambiguities and occlusions. Nonetheless, most existing works ignore these ambiguities and only estimate a single solution. In contrast, we generate a diverse set of hypotheses that represents the full posterior distribution of feasible 3D poses. To this end, we propose a normalizing flow based method that exploits the deterministic 3D-to-2D mapping to solve the ambiguous inverse 2D-to-3D problem. Additionally, uncertain detections and occlusions are effectively modeled by incorporating uncertainty information of the 2D detector as condition. Further keys to success are a learned 3D pose prior and a generalization of the best-of-M loss. We evaluate our approach on the two benchmark datasets Human3.6M and MPI-INF-3DHP, outperforming all comparable methods in most metrics. The implementation is available on GitHub.

We present a novel sequential Monte Carlo approach to online smoothing of additive functionals in a very general class of path-space models. Hitherto, the solutions proposed in the literature suffer from either long-term numerical instability due to particle-path degeneracy or, in the case that degeneracy is remedied by particle approximation of the so-called backward kernel, high computational demands. In order to balance optimally computational speed against numerical stability, we propose to furnish a (fast) naive particle smoother, propagating recursively a sample of particles and associated smoothing statistics, with an adaptive backward-sampling-based updating rule which allows the number of (costly) backward samples to be kept at a minimum. This yields a new, function-specific additive smoothing algorithm, AdaSmooth, which is computationally fast, numerically stable and easy to implement. The algorithm is provided with rigorous theoretical results guaranteeing its consistency, asymptotic normality and long-term stability as well as numerical results demonstrating empirically the clear superiority of AdaSmooth to existing algorithms.

The difficulty in specifying rewards for many real-world problems has led to an increased focus on learning rewards from human feedback, such as demonstrations. However, there are often many different reward functions that explain the human feedback, leaving agents with uncertainty over what the true reward function is. While most policy optimization approaches handle this uncertainty by optimizing for expected performance, many applications demand risk-averse behavior. We derive a novel policy gradient-style robust optimization approach, PG-BROIL, that optimizes a soft-robust objective that balances expected performance and risk. To the best of our knowledge, PG-BROIL is the first policy optimization algorithm robust to a distribution of reward hypotheses which can scale to continuous MDPs. Results suggest that PG-BROIL can produce a family of behaviors ranging from risk-neutral to risk-averse and outperforms state-of-the-art imitation learning algorithms when learning from ambiguous demonstrations by hedging against uncertainty, rather than seeking to uniquely identify the demonstrator's reward function.

In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years. These techniques (sometimes referred to as manifold learning) assume that the scattered input data is lying on a lower dimensional manifold, thus the high dimensionality problem can be overcome by learning the lower dimensionality behavior. However, in real life applications, data is often very noisy. In this work, we propose a method to approximate $\mathcal{M}$ a $d$-dimensional $C^{m+1}$ smooth submanifold of $\mathbb{R}^n$ ($d \ll n$) based upon noisy scattered data points (i.e., a data cloud). We assume that the data points are located "near" the lower dimensional manifold and suggest a non-linear moving least-squares projection on an approximating $d$-dimensional manifold. Under some mild assumptions, the resulting approximant is shown to be infinitely smooth and of high approximation order (i.e., $O(h^{m+1})$, where $h$ is the fill distance and $m$ is the degree of the local polynomial approximation). The method presented here assumes no analytic knowledge of the approximated manifold and the approximation algorithm is linear in the large dimension $n$. Furthermore, the approximating manifold can serve as a framework to perform operations directly on the high dimensional data in a computationally efficient manner. This way, the preparatory step of dimension reduction, which induces distortions to the data, can be avoided altogether.

Proximal Policy Optimization (PPO) is a highly popular model-free reinforcement learning (RL) approach. However, in continuous state and actions spaces and a Gaussian policy -- common in computer animation and robotics -- PPO is prone to getting stuck in local optima. In this paper, we observe a tendency of PPO to prematurely shrink the exploration variance, which naturally leads to slow progress. Motivated by this, we borrow ideas from CMA-ES, a black-box optimization method designed for intelligent adaptive Gaussian exploration, to derive PPO-CMA, a novel proximal policy optimization approach that can expand the exploration variance on objective function slopes and shrink the variance when close to the optimum. This is implemented by using separate neural networks for policy mean and variance and training the mean and variance in separate passes. Our experiments demonstrate a clear improvement over vanilla PPO in many difficult OpenAI Gym MuJoCo tasks.

Detecting objects and estimating their pose remains as one of the major challenges of the computer vision research community. There exists a compromise between localizing the objects and estimating their viewpoints. The detector ideally needs to be view-invariant, while the pose estimation process should be able to generalize towards the category-level. This work is an exploration of using deep learning models for solving both problems simultaneously. For doing so, we propose three novel deep learning architectures, which are able to perform a joint detection and pose estimation, where we gradually decouple the two tasks. We also investigate whether the pose estimation problem should be solved as a classification or regression problem, being this still an open question in the computer vision community. We detail a comparative analysis of all our solutions and the methods that currently define the state of the art for this problem. We use PASCAL3D+ and ObjectNet3D datasets to present the thorough experimental evaluation and main results. With the proposed models we achieve the state-of-the-art performance in both datasets.