Continual Learning (CL) sequentially learns new tasks like human beings, with the goal to achieve better Stability (S, remembering past tasks) and Plasticity (P, adapting to new tasks). Due to the fact that past training data is not available, it is valuable to explore the influence difference on S and P among training examples, which may improve the learning pattern towards better SP. Inspired by Influence Function (IF), we first study example influence via adding perturbation to example weight and computing the influence derivation. To avoid the storage and calculation burden of Hessian inverse in neural networks, we propose a simple yet effective MetaSP algorithm to simulate the two key steps in the computation of IF and obtain the S- and P-aware example influence. Moreover, we propose to fuse two kinds of example influence by solving a dual-objective optimization problem, and obtain a fused influence towards SP Pareto optimality. The fused influence can be used to control the update of model and optimize the storage of rehearsal. Empirical results show that our algorithm significantly outperforms state-of-the-art methods on both task- and class-incremental benchmark CL datasets.

This paper studies a framework, projected fixed-point method, for graph matching. The framework contains a class of popular graph matching algorithms, including graduated assignment (GA), integer projected fixed-point method (IPFP) and doubly stochastic projected fixed-point method (DSPFP). We propose an adaptive strategy to tune the step size parameter in this framework. Such a strategy improves these algorithms in efficiency and accuracy. Further, it guarantees the convergence of the underlying algorithms. Some preliminary analysis based on distance geometry seems to support that the optimal step size parameter has a high probability of 1 when graphs are fully connected. Secondly, it is observed that a popular projection method, softassign, is sensitive to graphs' cardinality(size). We proposed a dynamical softassign algorithm that is robust to graphs' cardinality. Combining the adaptive step size and the dynamical softassign, we propose a novel graph matching algorithm: the adaptive projected fixed-point method with dynamical softassign. Various experiments demonstrate that the proposed algorithm is significantly faster than several other state-of-art algorithms with no loss of accuracy.

Belief Propagation (BP) is an important message-passing algorithm for various reasoning tasks over graphical models, including solving the Constraint Optimization Problems (COPs). It has been shown that BP can achieve state-of-the-art performance on various benchmarks by mixing old and new messages before sending the new one, i.e., damping. However, existing methods of tuning a static damping factor for BP not only are laborious but also harm their performance. Moreover, existing BP algorithms treat each variable node's neighbors equally when composing a new message, which also limits their exploration ability. To address these issues, we seamlessly integrate BP, Gated Recurrent Units (GRUs), and Graph Attention Networks (GATs) within the message-passing framework to reason about dynamic weights and damping factors for composing new BP messages. Our model, Deep Attentive Belief Propagation (DABP), takes the factor graph and the BP messages in each iteration as the input and infers the optimal weights and damping factors through GRUs and GATs, followed by a multi-head attention layer. Furthermore, unlike existing neural-based BP variants, we propose a novel self-supervised learning algorithm for DABP with a smoothed solution cost, which does not require expensive training labels and also avoids the common out-of-distribution issue through efficient online learning. Extensive experiments show that our model significantly outperforms state-of-the-art baselines.

If robots are ever to achieve autonomous motion comparable to that exhibited by animals, they must acquire the ability to quickly recover motor behaviors when damage, malfunction, or environmental conditions compromise their ability to move effectively. We present an approach which allowed our robots and simulated robots to recover high-degree of freedom motor behaviors within a few dozen attempts. Our approach employs a behavior specification expressing the desired behaviors in terms as rank ordered differential constraints. We show how factoring these constraints through an encoding template produces a recipe for generalizing a previously optimized behavior to new circumstances in a form amenable to rapid learning. We further illustrate that adequate constraints are generically easy to determine in data-driven contexts. As illustration, we demonstrate our recovery approach on a physical 7 DOF hexapod robot, as well as a simulation of a 6 DOF 2D kinematic mechanism. In both cases we recovered a behavior functionally indistinguishable from the previously optimized motion.

We analyze the cumulative regret of the Dyadic Search algorithm of Bachoc et al. [2022]. In this section, we introduce the formal setting for our budget convex optimization problem. Given a bounded intervalI R, our goal is to minimize an unknown convex functionf I R picked by a possibly adversarial and adaptive environment by only requesting fuzzy evaluations of f. The interactions between the optimizer and the environment are described in Optimization Protocol 1. Optimization Protocol 1 input: A non-empty bounded interval I R (the domain of the unknown objective f) We stress that the environment is adaptive. The idea is that the more budget is invested, the more accurate approximation of the objectivef can be determined, in a quantifiable way.

Distributed machine learning enables scalability and computational offloading, but requires significant levels of communication. Consequently, communication efficiency in distributed learning settings is an important consideration, especially when the communications are wireless and battery-driven devices are employed. In this paper we develop a censoring-based heavy ball (CHB) method for distributed learning in a server-worker architecture. Each worker self-censors unless its local gradient is sufficiently different from the previously transmitted one. The significant practical advantages of the HB method for learning problems are well known, but the question of reducing communications has not been addressed. CHB takes advantage of the HB smoothing to eliminate reporting small changes, and provably achieves a linear convergence rate equivalent to that of the classical HB method for smooth and strongly convex objective functions. The convergence guarantee of CHB is theoretically justified for both convex and nonconvex cases. In addition we prove that, under some conditions, at least half of all communications can be eliminated without any impact on convergence rate. Extensive numerical results validate the communication efficiency of CHB on both synthetic and real datasets, for convex, nonconvex, and nondifferentiable cases. Given a target accuracy, CHB can significantly reduce the number of communications compared to existing algorithms, achieving the same accuracy without slowing down the optimization process.

Bandits with knapsacks (BwK) is an influential model of sequential decision-making under uncertainty that incorporates resource consumption constraints. In each round, the decision-maker observes an outcome consisting of a reward and a vector of nonnegative resource consumptions, and the budget of each resource is decremented by its consumption. In this paper we introduce a natural generalization of the stochastic BwK problem that allows non-monotonic resource utilization. In each round, the decision-maker observes an outcome consisting of a reward and a vector of resource drifts that can be positive, negative or zero, and the budget of each resource is incremented by its drift. Our main result is a Markov decision process (MDP) policy that has constant regret against a linear programming (LP) relaxation when the decision-maker knows the true outcome distributions. We build upon this to develop a learning algorithm that has logarithmic regret against the same LP relaxation when the decision-maker does not know the true outcome distributions. We also present a reduction from BwK to our model that shows our regret bound matches existing results.

This paper studies a natural generalization of the problem of minimizing a univariate convex function $f$ by querying its values sequentially. At each time-step $t$, the optimizer can invest a budget $b_t$ in a query point $X_t$ of their choice to obtain a fuzzy evaluation of $f$ at $X_t$ whose accuracy depends on the amount of budget invested in $X_t$ across times. This setting is motivated by the minimization of objectives whose values can only be determined approximately through lengthy or expensive computations. We design an any-time parameter-free algorithm called Dyadic Search, for which we prove near-optimal optimization error guarantees. As a byproduct of our analysis, we show that the classical dependence on the global Lipschitz constant in the error bounds is an artifact of the granularity of the budget. Finally, we illustrate our theoretical findings with numerical simulations.

We consider the problem of allocating a distribution of items to $n$ recipients where each recipient has to be allocated a fixed, prespecified fraction of all items, while ensuring that each recipient does not experience too much envy. We show that this problem can be formulated as a variant of the semi-discrete optimal transport (OT) problem, whose solution structure in this case has a concise representation and a simple geometric interpretation. Unlike existing literature that treats envy-freeness as a hard constraint, our formulation allows us to \emph{optimally} trade off efficiency and envy continuously. Additionally, we study the statistical properties of the space of our OT based allocation policies by showing a polynomial bound on the number of samples needed to approximate the optimal solution from samples. Our approach is suitable for large-scale fair allocation problems such as the blood donation matching problem, and we show numerically that it performs well on a prior realistic data simulator.

Reconstructing an accurate and consistent large-scale LiDAR point cloud map is crucial for robotics applications. The existing solution, pose graph optimization, though it is time-efficient, does not directly optimize the mapping consistency. LiDAR bundle adjustment (BA) has been recently proposed to resolve this issue; however, it is too time-consuming on large-scale maps. To mitigate this problem, this paper presents a globally consistent and efficient mapping method suitable for large-scale maps. Our proposed work consists of a bottom-up hierarchical BA and a top-down pose graph optimization, which combines the advantages of both methods. With the hierarchical design, we solve multiple BA problems with a much smaller Hessian matrix size than the original BA; with the pose graph optimization, we smoothly and efficiently update the LiDAR poses. The effectiveness and robustness of our proposed approach have been validated on multiple spatially and timely large-scale public spinning LiDAR datasets, i.e., KITTI, MulRan and Newer College, and self-collected solid-state LiDAR datasets under structured and unstructured scenes. With proper setups, we demonstrate our work could generate a globally consistent map with around 12% of the sequence time.