Safe reinforcement learning (RL) aims to solve an optimal control problem under safety constraints. Existing $\textit{direct}$ safe RL methods use the original constraint throughout the learning process. They either lack theoretical guarantees of the policy during iteration or suffer from infeasibility problems. To address this issue, we propose an $\textit{indirect}$ safe RL method called feasible policy iteration (FPI) that iteratively uses the feasible region of the last policy to constrain the current policy. The feasible region is represented by a feasibility function called constraint decay function (CDF). The core of FPI is a region-wise policy update rule called feasible policy improvement, which maximizes the return under the constraint of the CDF inside the feasible region and minimizes the CDF outside the feasible region. This update rule is always feasible and ensures that the feasible region monotonically expands and the state-value function monotonically increases inside the feasible region. Using the feasible Bellman equation, we prove that FPI converges to the maximum feasible region and the optimal state-value function. Experiments on classic control tasks and Safety Gym show that our algorithms achieve lower constraint violations and comparable or higher performance than the baselines.

Over the years, various benchmark suites have been proposed, in which different global function properties are represented, such The GKLS generator is one of the most used testbeds for benchmarking as multi-modality, separability, ill-conditioning, and various other global optimization algorithms. In this paper, we conduct both types of global structures. In the evolutionary computation community, a computational analysis and the Exploratory Landscape Analysis the two most utilized benchmark sets are the Black-Box (ELA) of the GKLS generator. We utilize both canonically used and Optimization Benchmarking (BBOB) suite [5] which is now part of newly generated classes of GKLS-generated problems and show the COCO platform [6], and the suites that were presented at the their use in benchmarking three state-of-the-art methods (from evolutionary Congress on Evolutionary Computation (CEC) competitions (which and deterministic communities) in dimensions 5 and 10. started in 2005 and continue to this day) [9]. As was shown in [3], We show that the GKLS generator produces "needle in a haystack" the characteristics of the functions used in these two benchmarks type problems that become extremely difficult to optimize in higher are quite different. The CEC benchmarks are constructed by using dimensions. Furthermore, we conduct the ELA on the GKLS generator similar subfunctions, which possibly gives an advantage to methods and then compare it to the ELA of two other widely used that perform well on these fewer subfunctions. It was also found benchmark sets (BBOB and CEC 2014), and discuss the meaningfulness that the CEC functions share more similarities among themselves of the results.

Base placement optimization (BPO) is a fundamental capability for mobile manipulation and has been researched for decades. However, it is still very challenging for some reasons. First, compared with humans, current robots are extremely inflexible, and therefore have higher requirements on the accuracy of base placements (BPs). Second, the BP and task constraints are coupled with each other. The optimal BP depends on the task constraints, and in BP will affect task constraints in turn. More tricky is that some task constraints are flexible and non-deterministic. Third, except for fulfilling tasks, some other performance metrics such as optimal energy consumption and minimal execution time need to be considered, which makes the BPO problem even more complicated. In this paper, a Scale-like disc (SLD) representation of the workspace is used to decouple task constraints and BPs. To evaluate reachability and return optimal working pose over SLDs, a reachability map (RM) is constructed offline. In order to optimize the objectives of coverage, manipulability, and time cost simultaneously, this paper formulates the BPO as a multi-objective optimization problem (MOOP). Among them, the time optimal objective is modeled as a traveling salesman problem (TSP), which is more in line with the actual situation. The evolutionary method is used to solve the MOOP. Besides, to ensure the validity and optimality of the solution, collision detection is performed on the candidate BPs, and solutions from BPO are further fine-tuned according to the specific given task. Finally, the proposed method is used to solve a real-world toilet coverage cleaning task. Experiments show that the optimized BPs can significantly improve the coverage and efficiency of the task.

Incentive mechanism is crucial for federated learning (FL) when rational clients do not have the same interests in the global model as the server. However, due to system heterogeneity and limited budget, it is generally impractical for the server to incentivize all clients to participate in all training rounds (known as full participation). The existing FL incentive mechanisms are typically designed by stimulating a fixed subset of clients based on their data quantity or system resources. Hence, FL is performed only using this subset of clients throughout the entire training process, leading to a biased model because of data heterogeneity. This paper proposes a game theoretic incentive mechanism for FL with randomized client participation, where the server adopts a customized pricing strategy that motivates different clients to join with different participation levels (probabilities) for obtaining an unbiased and high performance model. Each client responds to the server's monetary incentive by choosing its best participation level, to maximize its profit based on not only the incurred local cost but also its intrinsic value for the global model. To effectively evaluate clients' contribution to the model performance, we derive a new convergence bound which analytically predicts how clients' arbitrary participation levels and their heterogeneous data affect the model performance. By solving a non-convex optimization problem, our analysis reveals that the intrinsic value leads to the interesting possibility of bidirectional payment between the server and clients. Experimental results using real datasets on a hardware prototype demonstrate the superiority of our mechanism in achieving higher model performance for the server as well as higher profits for the clients.

Tail Averaging improves on Polyak averaging's non-asymptotic behaviour by excluding a number of leading iterates of stochastic optimization from its calculations. In practice, with a finite number of optimization steps and a learning rate that cannot be annealed to zero, Tail Averaging can get much closer to a local minimum point of the training loss than either the individual iterates or the Polyak average. However, the number of leading iterates to ignore is an important hyperparameter, and starting averaging too early or too late leads to inefficient use of resources or suboptimal solutions. Our work focusses on improving generalization, which makes setting this hyperparameter even more difficult, especially in the presence of other hyperparameters and overfitting. Furthermore, before averaging starts, the loss is only weakly informative of the final performance, which makes early stopping unreliable. To alleviate these problems, we propose an anytime variant of Tail Averaging intended for improving generalization not pure optimization, that has no hyperparameters and approximates the optimal tail at all optimization steps. Our algorithm is based on two running averages with adaptive lengths bounded in terms of the optimal tail length, one of which achieves approximate optimality with some regularity. Requiring only the additional storage for two sets of weights and periodic evaluation of the loss, the proposed Two-Tailed Averaging algorithm is a practical and widely applicable method for improving generalization.

In distributed machine learning, a central node outsources computationally expensive calculations to external worker nodes. The properties of optimization procedures like stochastic gradient descent (SGD) can be leveraged to mitigate the effect of unresponsive or slow workers called stragglers, that otherwise degrade the benefit of outsourcing the computation. This can be done by only waiting for a subset of the workers to finish their computation at each iteration of the algorithm. Previous works proposed to adapt the number of workers to wait for as the algorithm evolves to optimize the speed of convergence. In contrast, we model the communication and computation times using independent random variables. Considering this model, we construct a novel scheme that adapts both the number of workers and the computation load throughout the run-time of the algorithm. Consequently, we improve the convergence speed of distributed SGD while significantly reducing the computation load, at the expense of a slight increase in communication load.

In this paper we study a class of constrained minimax problems. In particular, we propose a first-order augmented Lagrangian method for solving them, whose subproblems turn out to be a much simpler structured minimax problem and are suitably solved by a first-order method recently developed in [26] by the authors. Under some suitable assumptions, an \emph{operation complexity} of ${\cal O}(\varepsilon^{-4}\log\varepsilon^{-1})$, measured by its fundamental operations, is established for the first-order augmented Lagrangian method for finding an $\varepsilon$-KKT solution of the constrained minimax problems.

AUC is a common metric for evaluating the performance of a classifier. However, most classifiers are trained with cross entropy, and it does not optimize the AUC metric directly, which leaves a gap between the training and evaluation stage. In this paper, we propose the PDAOM loss, a Personalized and Differentiable AUC Optimization method with Maximum violation, which can be directly applied when training a binary classifier and optimized with gradient-based methods. Specifically, we construct the pairwise exponential loss with difficult pair of positive and negative samples within sub-batches grouped by user ID, aiming to guide the classifier to pay attention to the relation between hard-distinguished pairs of opposite samples from the perspective of independent users. Compared to the origin form of pairwise exponential loss, the proposed PDAOM loss not only improves the AUC and GAUC metrics in the offline evaluation, but also reduces the computation complexity of the training objective. Furthermore, online evaluation of the PDAOM loss on the 'Guess What You Like' feed recommendation application in Meituan manifests 1.40% increase in click count and 0.65% increase in order count compared to the baseline model, which is a significant improvement in this well-developed online life service recommendation system.

In most image retrieval systems, images include various high-level semantics, called tags or annotations. Virtually all the state-of-the-art image annotation methods that handle imbalanced labeling are search-based techniques which are time-consuming. In this paper, a novel coupled dictionary learning approach is proposed to learn a limited number of visual prototypes and their corresponding semantics simultaneously. This approach leads to a real-time image annotation procedure. Another contribution of this paper is that utilizes a marginalized loss function instead of the squared loss function that is inappropriate for image annotation with imbalanced labels. We have employed a marginalized loss function in our method to leverage a simple and effective method of prototype updating. Meanwhile, we have introduced ${\ell}_1$ regularization on semantic prototypes to preserve the sparse and imbalanced nature of labels in learned semantic prototypes. Finally, comprehensive experimental results on various datasets demonstrate the efficiency of the proposed method for image annotation tasks in terms of accuracy and time. The reference implementation is publicly available on https://github.com/hamid-amiri/MCDL-Image-Annotation.

We develop a novel graph-based trainable framework to maximize the weighted sum energy efficiency (WSEE) for power allocation in wireless communication networks. To address the non-convex nature of the problem, the proposed method consists of modular structures inspired by a classical iterative suboptimal approach and enhanced with learnable components. More precisely, we propose a deep unfolding of the successive concave approximation (SCA) method. In our unfolded SCA (USCA) framework, the originally preset parameters are now learnable via graph convolutional neural networks (GCNs) that directly exploit multi-user channel state information as the underlying graph adjacency matrix. We show the permutation equivariance of the proposed architecture, which is a desirable property for models applied to wireless network data. The USCA framework is trained through a stochastic gradient descent approach using a progressive training strategy. The unsupervised loss is carefully devised to feature the monotonic property of the objective under maximum power constraints. Comprehensive numerical results demonstrate its generalizability across different network topologies of varying size, density, and channel distribution. Thorough comparisons illustrate the improved performance and robustness of USCA over state-of-the-art benchmarks.