Lifelong multitask learning poses considerable challenges in terms of effectiveness (minimizing prediction errors for all tasks) and overall computational tractability for real-time performance. This paper addresses continuous lifelong multitask learning by jointly re-estimating the inter-task relations (output kernel) and the per-task model parameters at each round, assuming data arrives in a streaming fashion. A new algorithm called Online Output Kernel Learning Algorithm (OOKLA) for lifelong learning setting is proposed. To avoid the memory explosion, a robust budget-limited versions of the proposed algorithm is introduced, which efficiently utilizes the relationships between the tasks to bound the total number of representative examples in the support set. In addition, a two-stage budgeted scheme for efficiently tackling the task-specific budget constraints in lifelong learning is proposed. Empirical results over three datasets indicate superior AUC performance for OOKLA and its budget-limited cousins over strong baselines.
CONTRIBUTION
The main contribution of the paper is not clearly stated.  To the reviewer, It seems “life-long learning” is the same as “online learning”.  However, the whole paper does not define what “life-long learning” is.
The limited budget scheme is well established in the literature. 
1. J. Hu, H. Yang, I. King, M. R. Lyu, and A. M.-C. So. Kernelized online imbalanced learning with fixed budgets. In AAAI, Austin Texas, USA, Jan. 25-30 2015.  
2. Y. Engel, S. Mannor, and R. Meir. The kernel recursive least-squares algorithm. IEEE Transactions on Signal Processing, 52(8):2275–2285, 2004.
It is not clear what the new proposal in the paper.
WRITING QUALITY
The paper is not well written in a good shape. Many meanings of the equations are not stated clearly, e.g., $phi$ in eq. (7). Furthermore, the equation in algorithm 2 is not well formatted. 
DETAILED COMMENTS
1. The mapping function $phi$ appears in Eq. (1) without definition.
2. The last equation in pp. 3 defines the decision function f by an inner product. In the equation, the notation x_t and i_t is not clearly defined.  More seriously, a comma is missed in the definition of the inner product.
3. Some equations are labeled but never referenced, e.g., Eq. (4).
4. The physical meaning of Eq.(7) is unclear.  However, this equation is the key proposal of the paper.   For example, what is the output of the Eq. (7)? What is the main objective of Eq. (7)?  Moreover, what support vectors should be removed by optimizing Eq. (7)?  One main issue is that the notation $phi$ is not clearly defined.   The computation of f-y_r\phi(s_r) makes it hard to understand.  Especially,  the dimension of $phi$ in Eq.(7) is unknown. 
ABOUT EXPERIMENTS
1.	It is unclear how to tune the hyperparameters.
2.	In Table 1, the results only report the standard deviation of AUC. No standard deviations of nSV and Time are reported.