Four years ago, an experimental system known as PilotNet became the first NVIDIA system to steer an autonomous car along a roadway. This system represents a departure from the classical approach for self-driving in which the process is manually decomposed into a series of modules, each performing a different task. In PilotNet, on the other hand, a single deep neural network (DNN) takes pixels as input and produces a desired vehicle trajectory as output; there are no distinct internal modules connected by human-designed interfaces. We believe that handcrafted interfaces ultimately limit performance by restricting information flow through the system and that a learned approach, in combination with other artificial intelligence systems that add redundancy, will lead to better overall performing systems. We continue to conduct research toward that goal. This document describes the PilotNet lane-keeping effort, carried out over the past five years by our NVIDIA PilotNet group in Holmdel, New Jersey. Here we present a snapshot of system status in mid-2020 and highlight some of the work done by the PilotNet group.

In this paper, we consider three typical optimization problems with a convex loss function and a nonconvex sparse penalty or constraint. For the sparse penalized problem, we prove that fi nding an O (n(c1)d(c2))-optimal solution to an n x d problem is strongly NP-hard for any c(1), c(2) epsilon [0; 1) such that c(1) + c(2) < 1. For two constrained versions of the sparse optimization problem, we show that it is intractable to approximately compute a solution path associated with increasing values of some tuning parameter. The hardness results apply to a broad class of loss functions and sparse penalties. They suggest that one cannot even approximately solve these three problems in polynomial time, unless P = NP.

Approximate linear programming (ALP) represents one of the major algorithmic families to solve large-scale Markov decision processes (MDP). In this work, we study a primal-dual formulation of the ALP, and develop a scalable, model-free algorithm called bilinear $\pi$ learning for reinforcement learning when a sampling oracle is provided. This algorithm enjoys a number of advantages. First, it adopts (bi)linear models to represent the high-dimensional value function and state-action distributions, using given state and action features. Its run-time complexity depends on the number of features, not the size of the underlying MDPs. Second, it operates in a fully online fashion without having to store any sample, thus having minimal memory footprint. Third, we prove that it is sample-efficient, solving for the optimal policy to high precision with a sample complexity linear in the dimension of the parameter space.

PROBLEM TO BE SOLVED: To provide a method and system for improving object detection performance.SOLUTION: A method for detecting an object in an image includes extracting a first feature vector from a first region of an image using a first subnetwork, determining a second region of the image by resizing the first region into a fixed ratio, wherein a size of the first region is smaller than a size of the second region, extracting a second feature vector from the second region of the image using a second subnetwork, classifying a class of the object using a third subnetwork on a basis of the first feature vector and the second feature vector, and determining the class of object in the first region according to a result of the classification. The first subnetwork, the second subnetwork, and the third subnetwork form a neural network. The steps of the method are performed by a processor.SELECTED DRAWING: Figure 2

In this paper, we propose a fully decentralized authentication and revocation scheme(f-DMA) based on multi-authority attribute-based encryption that can be used in data sharing systems with multiple distrusted authorizes. This scheme establishes a fully decentralized secret key generation and key distribution systems, which eliminates the security risk on central authority(CA) compromise and is resilient to authority and user collusion attacks. Our system also provides computation efficient revocation that can achieve both specific user revocation and attribute revocation. We prove our scheme correct under the Decisional Bilinear Diffie-Hellman (DBDH) assumption; we also include a complete end-to-end implementation that demonstrates the practical efficacy of our technique.

We study the computational complexity of the infinite-horizon discounted-reward Markov Decision Problem (MDP) with a finite state space |𝒮| and a finite action space |𝒜|. We show that any randomized algorithm needs a running time at least Ω(|𝒮|^2|𝒜|) to compute an ϵ-optimal policy with high probability. We consider two variants of the MDP where the input is given in specific data structures, including arrays of cumulative probabilities and binary trees of transition probabilities. For these cases, we show that the complexity lower bound reduces to Ω( |𝒮| |𝒜|/ϵ). These results reveal a surprising observation that the computational complexity of the MDP depends on the data structure of input.

Existing object detection literature focuses on detecting a big object covering a large part of an image. The problem of detecting a small object covering a small part of an image is largely ignored. As a result, the state-of-the-art object detection algorithm renders unsatisfactory performance as applied to detect small objects in images. In this paper, we dedicate an effort to bridge the gap. We first compose a benchmark dataset tailored for the small object detection problem to better evaluate the small object detection performance. We then augment the state-of-the-art R-CNN algorithm with a context model and a small region proposal generator to improve the small object detection performance. We conduct extensive experimental validations for studying various design choices. Experiment results show that the augmented R-CNN algorithm improves the mean average precision by 29.8% over the original R-CNN algorithm on detecting small objects.

We study the online estimation of the optimal policy of a Markov decision process (MDP). We propose a class of Stochastic Primal-Dual (SPD) methods which exploit the inherent minimax duality of Bellman equations. The SPD methods update a few coordinates of the value and policy estimates as a new state transition is observed. These methods use small storage and has low computational complexity per iteration. The SPD methods find an absolute-$\epsilon$-optimal policy, with high probability, using $\mathcal{O}\left(\frac{|\mathcal{S}|^4 |\mathcal{A}|^2\sigma^2 }{(1-\gamma)^6\epsilon^2} \right)$ iterations/samples for the infinite-horizon discounted-reward MDP and $\mathcal{O}\left(\frac{|\mathcal{S}|^4 |\mathcal{A}|^2H^6\sigma^2 }{\epsilon^2} \right)$ for the finite-horizon MDP.

We consider the online solution of discounted Markov decision processes (MDP). We focus on the black-box learning model where transition probabilities and state transition cost are unknown. Instead, a simulator is available to generate random state transitions under given actions. We propose a stochastic primal-dual algorithm for solving the linear formulation of the Bellman equation. The algorithm updates the primal and dual iterates by using sample state transitions and sample costs generated by the simulator. We provide a thresholding procedure that recovers the exact optimal policy from the dual iterates with high probability.

Today, there are two major paradigms for vision-based autonomous driving systems: mediated perception approaches that parse an entire scene to make a driving decision, and behavior reflex approaches that directly map an input image to a driving action by a regressor. In this paper, we propose a third paradigm: a direct perception approach to estimate the affordance for driving. We propose to map an input image to a small number of key perception indicators that directly relate to the affordance of a road/traffic state for driving. Our representation provides a set of compact yet complete descriptions of the scene to enable a simple controller to drive autonomously. Falling in between the two extremes of mediated perception and behavior reflex, we argue that our direct perception representation provides the right level of abstraction. To demonstrate this, we train a deep Convolutional Neural Network using recording from 12 hours of human driving in a video game and show that our model can work well to drive a car in a very diverse set of virtual environments. We also train a model for car distance estimation on the KITTI dataset. Results show that our direct perception approach can generalize well to real driving images. Source code and data are available on our project website.

In this note, we consider the regularize $L_q$-minimization problem ($q\ge 1$) with a general penalty function. We show that if the penalty function is concave but not linear in a neighborhood of zero, then the optimization problem is strongly NP-hard. This result answers the complexity of many regularized optimization problems studied in the literature. It implies that it is impossible to have a fully polynomial-time approximation scheme (FPTAS) for a large class of regularization problems unless P = NP.

Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex sets. We propose a class of algorithms that perform both stochastic gradient descent and random feasibility updates simultaneously. At every iteration, the algorithms sample a number of projection points onto a randomly selected small subsets of all constraints. Three feasibility update schemes are considered: averaging over random projected points, projecting onto the most distant sample, projecting onto a special polyhedral set constructed based on sample points. We prove the almost sure convergence of these algorithms, and analyze the iterates' feasibility error and optimality error, respectively. We provide new convergence rate benchmarks for stochastic first-order optimization with many constraints. The rate analysis and numerical experiments reveal that the algorithm using the polyhedral-set projection scheme is the most efficient one within known algorithms.