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We present QuantumSync, the first quantum algorithm for solving a synchronization problem in the context of computer vision. In particular, we focus on permutation synchronization which involves solving a non-convex optimization problem in discrete variables. We start by formulating synchronization into a quadratic unconstrained binary optimization problem (QUBO). While such formulation respects the binary nature of the problem, ensuring that the result is a set of permutations requires extra care. Hence, we: (I) show how to insert permutation constraints into a QUBO problem and (ii) solve the constrained QUBO problem on the current generation of the adiabatic quantum computers D-Wave. Thanks to the quantum annealing, we guarantee global optimality with high probability while sampling the energy landscape to yield confidence estimates. Our proof-of-concepts realization on the adiabatic D-Wave computer demonstrates that quantum machines offer a promising way to solve the prevalent yet difficult synchronization problems.

A fascinating aspect of nature lies in its ability to produce a large and diverse collection of organisms that are all high-performing in their niche. By contrast, most AI algorithms focus on finding a single efficient solution to a given problem. Aiming for diversity in addition to performance is a convenient way to deal with the exploration-exploitation trade-off that plays a central role in learning. It also allows for increased robustness when the returned collection contains several working solutions to the considered problem, making it well-suited for real applications such as robotics. Quality-Diversity (QD) methods are evolutionary algorithms designed for this purpose. This paper proposes a novel algorithm, QD - PG , which combines the strength of Policy Gradient algorithms and Quality Diversity approaches to produce a collection of diverse and high-performing neural policies in continuous control environments. The main contribution of this work is the introduction of a Diversity Policy Gradient (DPG) that exploits information at the time-step level to thrive policies towards more diversity in a sample-efficient manner. Specifically, QD - PG selects neural controllers from a MAP - E lites grid and uses two gradient-based mutation operators to improve both quality and diversity, resulting in stable population updates. Our results demonstrate that QD - PG generates collections of diverse solutions that solve challenging exploration and control problems while being two orders of magnitude more sample-efficient than its evolutionary competitors.

A common approach to tackle a combinatorial optimization problem is to first solve a continuous relaxation and then round the obtained fractional solution. For the latter, the framework of contention resolution schemes (or CR schemes), introduced by Chekuri, Vondrak, and Zenklusen, is a general and successful tool. A CR scheme takes a fractional point $x$ in a relaxation polytope, rounds each coordinate $x_i$ independently to get a possibly non-feasible set, and then drops some elements in order to satisfy the independence constraints. Intuitively, a CR scheme is $c$-balanced if every element $i$ is selected with probability at least $c \cdot x_i$. It is known that general matroids admit a $(1-1/e)$-balanced CR scheme, and that this is (asymptotically) optimal. This is in particular true for the special case of uniform matroids of rank one. In this work, we provide a simple and explicit monotone CR scheme with a balancedness of $1 - \binom{n}{k}\:\left(1-\frac{k}{n}\right)^{n+1-k}\:\left(\frac{k}{n}\right)^k$, and show that this is optimal. As $n$ grows, this expression converges from above to $1 - e^{-k}k^k/k!$. While this asymptotic bound can be obtained by combining previously known results, these require defining an exponential-sized linear program, as well as using random sampling and the ellipsoid algorithm. Our procedure, on the other hand, has the advantage of being simple and explicit. Moreover, this scheme generalizes into an optimal CR scheme for partition matroids.

A recent line of ground-breaking results for permutation-based SGD has corroborated a widely observed phenomenon: random permutations offer faster convergence than with-replacement sampling. However, is random optimal? We show that this depends heavily on what functions we are optimizing, and the convergence gap between optimal and random permutations can vary from exponential to nonexistent. We first show that for 1-dimensional strongly convex functions, with smooth second derivatives, there exist permutations that offer exponentially faster convergence compared to random. However, for general strongly convex functions, random permutations are optimal. Finally, we show that for quadratic, strongly-convex functions, there are easy-to-construct permutations that lead to accelerated convergence compared to random. Our results suggest that a general convergence characterization of optimal permutations cannot capture the nuances of individual function classes, and can mistakenly indicate that one cannot do much better than random.

We propose a method for object-aware 3D egocentric pose estimation that tightly integrates kinematics modeling, dynamics modeling, and scene object information. Unlike prior kinematics or dynamics-based approaches where the two components are used disjointly, we synergize the two approaches via dynamics-regulated training. At each timestep, a kinematic model is used to provide a target pose using video evidence and simulation state. Then, a prelearned dynamics model attempts to mimic the kinematic pose in a physics simulator. By comparing the pose instructed by the kinematic model against the pose generated by the dynamics model, we can use their misalignment to further improve the kinematic model. By factoring in the 6DoF pose of objects (e.g., chairs, boxes) in the scene, we demonstrate for the first time, the ability to estimate physically-plausible 3D human-object interactions using a single wearable camera. We evaluate our egocentric pose estimation method in both controlled laboratory settings and real-world scenarios.

Constrained tensor and matrix factorization models allow to extract interpretable patterns from multiway data. Therefore identifiability properties and efficient algorithms for constrained low-rank approximations are nowadays important research topics. This work deals with columns of factor matrices of a low-rank approximation being sparse in a known and possibly overcomplete basis, a model coined as Dictionary-based Low-Rank Approximation (DLRA). While earlier contributions focused on finding factor columns inside a dictionary of candidate columns, i.e. one-sparse approximations, this work is the first to tackle DLRA with sparsity larger than one. I propose to focus on the sparse-coding subproblem coined Mixed Sparse-Coding (MSC) that emerges when solving DLRA with an alternating optimization strategy. Several algorithms based on sparse-coding heuristics (greedy methods, convex relaxations) are provided to solve MSC. The performance of these heuristics is evaluated on simulated data. Then, I show how to adapt an efficient MSC solver based on the LASSO to compute Dictionary-based Matrix Factorization and Canonical Polyadic Decomposition in the context of hyperspectral image processing and chemometrics. These experiments suggest that DLRA extends the modeling capabilities of low-rank approximations, helps reducing estimation variance and enhances the identifiability and interpretability of estimated factors.

We study the problem of learning in the stochastic shortest path (SSP) setting, where an agent seeks to minimize the expected cost accumulated before reaching a goal state. We design a novel model-based algorithm EB-SSP that carefully skews the empirical transitions and perturbs the empirical costs with an exploration bonus to guarantee both optimism and convergence of the associated value iteration scheme. We prove that EB-SSP achieves the minimax regret rate $\widetilde{O}(B_{\star} \sqrt{S A K})$, where $K$ is the number of episodes, $S$ is the number of states, $A$ is the number of actions and $B_{\star}$ bounds the expected cumulative cost of the optimal policy from any state, thus closing the gap with the lower bound. Interestingly, EB-SSP obtains this result while being parameter-free, i.e., it does not require any prior knowledge of $B_{\star}$, nor of $T_{\star}$ which bounds the expected time-to-goal of the optimal policy from any state. Furthermore, we illustrate various cases (e.g., positive costs, or general costs when an order-accurate estimate of $T_{\star}$ is available) where the regret only contains a logarithmic dependence on $T_{\star}$, thus yielding the first horizon-free regret bound beyond the finite-horizon MDP setting.

Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale datasets. Among the possible strategies to alleviate this issue, practitioners can rely on computing estimates of these distances over subsets of data, {\em i.e.} minibatches. While computationally appealing, we highlight in this paper some limits of this strategy, arguing it can lead to undesirable smoothing effects. As an alternative, we suggest that the same minibatch strategy coupled with unbalanced optimal transport can yield more robust behavior. We discuss the associated theoretical properties, such as unbiased estimators, existence of gradients and concentration bounds. Our experimental study shows that in challenging problems associated to domain adaptation, the use of unbalanced optimal transport leads to significantly better results, competing with or surpassing recent baselines.

We present an end-to-end framework for solving the Vehicle Routing Problem (VRP) using reinforcement learning. In this approach, we train a single model that finds near-optimal solutions for problem instances sampled from a given distribution, only by observing the reward signals and following feasibility rules. Our model represents a parameterized stochastic policy, and by applying a policy gradient algorithm to optimize its parameters, the trained model produces the solution as a sequence of consecutive actions in real time, without the need to re-train for every new problem instance. On capacitated VRP, our approach outperforms classical heuristics and Google's OR-Tools on medium-sized instances in solution quality with comparable computation time (after training). We demonstrate how our approach can handle problems with split delivery and explore the effect of such deliveries on the solution quality. Our proposed framework can be applied to other variants of the VRP such as the stochastic VRP, and has the potential to be applied more generally to combinatorial optimization problems.

Deep reinforcement learning (RL) methods generally engage in exploratory behavior through noise injection in the action space. An alternative is to add noise directly to the agent's parameters, which can lead to more consistent exploration and a richer set of behaviors. Methods such as evolutionary strategies use parameter perturbations, but discard all temporal structure in the process and require significantly more samples. Combining parameter noise with traditional RL methods allows to combine the best of both worlds. We demonstrate that both off- and on-policy methods benefit from this approach through experimental comparison of DQN, DDPG, and TRPO on high-dimensional discrete action environments as well as continuous control tasks. Our results show that RL with parameter noise learns more efficiently than traditional RL with action space noise and evolutionary strategies individually.