Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal of the downstream optimization problem. Recently, decision-focused prediction approaches, such as SPO+ and direct optimization, have been proposed to fill this gap. However, they cannot directly handle the soft constraints with the $max$ operator required in many real-world objectives. This paper proposes a novel analytically differentiable surrogate objective framework for real-world linear and semi-definite negative quadratic programming problems with soft linear and non-negative hard constraints. This framework gives the theoretical bounds on constraints' multipliers, and derives the closed-form solution with respect to predictive parameters and thus gradients for any variable in the problem. We evaluate our method in three applications extended with soft constraints: synthetic linear programming, portfolio optimization, and resource provisioning, demonstrating that our method outperforms traditional two-staged methods and other decision-focused approaches.

Class incremental learning refers to a special multi-class classification task, in which the number of classes is not fixed but is increasing with the continual arrival of new data. Existing researches mainly focused on solving catastrophic forgetting problem in class incremental learning. To this end, however, these models still require the old classes cached in the auxiliary data structure or models, which is inefficient in space or time. In this paper, it is the first time to discuss the difficulty without support of old classes in class incremental learning, which is called as softmax suppression problem. To address these challenges, we develop a new model named Label Mapping with Response Consolidation (LMRC), which need not access the old classes anymore. We propose the Label Mapping algorithm combined with the multi-head neural network for mitigating the softmax suppression problem, and propose the Response Consolidation method to overcome the catastrophic forgetting problem. Experimental results on the benchmark datasets show that our proposed method achieves much better performance compared to the related methods in different scenarios.