We study a new method (``Diverse Ensemble Evolution (DivE$^2$)'') to train an ensemble of machine learning models that assigns data to models at each training epoch based on each model's current expertise and an intra-and inter-model diversity reward. DivE$^2$ schedules, over the course of training epochs, the relative importance of these characteristics; it starts by selecting easy samples for each model, and then gradually adjusts towards the models having specialized and complementary expertise on subsets of the training data, thereby encouraging high accuracy of the ensemble. We utilize an intra-model diversity term on data assigned to each model, and an inter-model diversity term on data assigned to pairs of models, to penalize both within-model and cross-model redundancy. We formulate the data-model marriage problem as a generalized bipartite matching, represented as submodular maximization subject to two matroid constraints. DivE$^2$ solves a sequence of continuous-combinatorial optimizations with slowly varying objectives and constraints. The combinatorial part handles the data-model marriage while the continuous part updates model parameters based on the assignments. In experiments, DivE$^2$ outperforms other ensemble training methods under a variety of model aggregation techniques, while also maintaining competitive efficiency.

The observation of WikiHow is represented in exactly the same way with Zhang et al. [2023]. Table 1: Patterns of WebShop pages Pattern Description search The page to search for an item itemlisting The page listing the search results item The information page of a specific item others The item description page, item feature page, and review pageThe similarity lookup table is defined in Table 2. 1 Table 2: Lookup table of the page similarity of WebShop search itemlisting item others search 1 0 0 0 itemlisting 0 1 0 0 item 0 0 1 0.3 others 0 0 0.3 1 2.2 Lookup table of the instruction similarity function of WikiHow Table 3. Table 3: Patterns of WikiHow instructions Pattern Name Pattern Template search Search an article to learn . . . Owing to the limit of budgets, a subset of only 20 tasks is sampled from the full test set. The visualization is available in Figure 2. It can be seen that the performance of R However, there seems to be a saturation for the performance, which may be attributed to the limited number of the active exemplars and training tasks. The saturation of the average reward comes later than that of the success rate. Double Q-Learning [van Hasselt, 2010] is usually leveraged to ameliorate over-estimation for lookup-based Q-Learning.

We list detailed hyper-parameter settings here for reproducibility.