Like generic multi-task learning, continual learning has the nature of multi-objective optimization, and therefore faces a trade-off between the performance of different tasks. That is, to optimize for the current task distribution, it may need to compromise performance on some previous tasks. This means that there exist multiple models that are Pareto-optimal at different times, each addressing a distinct task performance trade-off. Researchers have discussed how to train particular models to address specific trade-off preferences. However, existing algorithms require training overheads proportional to the number of preferences -- a large burden when there are multiple, possibly infinitely many, preferences. As a response, we propose Imprecise Bayesian Continual Learning (IBCL). Upon a new task, IBCL (1) updates a knowledge base in the form of a convex hull of model parameter distributions and (2) obtains particular models to address task trade-off preferences with zero-shot. That is, IBCL does not require any additional training overhead to generate preference-addressing models from its knowledge base. We show that models obtained by IBCL have guarantees in identifying the Pareto optimal parameters. Moreover, experiments on standard image classification and NLP tasks support this guarantee. Statistically, IBCL improves average per-task accuracy by at most 23\% and peak per-task accuracy by at most 15\% with respect to the baseline methods, with steadily near-zero or positive backward transfer. Most importantly, IBCL significantly reduces the training overhead from training 1 model per preference to at most 3 models for all preferences.

翻译：与通用的多任务学习类似，持续学习本质上也属于多目标优化问题，因此面临不同任务性能之间的权衡。即，为优化当前任务分布，可能需要牺牲某些先前任务的性能。这意味着存在多个在不同时间点达到帕累托最优的模型，每个模型对应不同的任务性能权衡。研究者已探讨如何训练特定模型以应对特定权衡偏好。然而，现有算法需要与偏好数量成正比的训练开销——当存在多个（甚至无限个）偏好时，这将成为沉重负担。为此，我们提出非精确贝叶斯持续学习（IBCL）。面对新任务时，IBCL（1）以模型参数分布的凸包形式更新知识库，并（2）通过零样本方式获取应对任务权衡偏好的特定模型。即，IBCL无需额外训练开销即可从其知识库生成偏好匹配模型。我们证明了IBCL获得的模型具备识别帕累托最优参数的保证。此外，标准图像分类和自然语言处理任务的实验支持了该保证。统计结果显示，与基线方法相比，IBCL将每任务平均准确率最高提升23%，峰值准确率最高提升15%，且保持持续接近零或正向的后向迁移。最重要的是，IBCL将训练开销从每个偏好训练1个模型显著降低至所有偏好最多仅需3个模型。