Contextual Bandit Approach-based Recommendation System for Personalized Web-based Services

Figures & data

Table 1. Symbol table

SYMBOL	MEANING
$\alpha$	Exploration Parameter
$M$	Number of Clusters
$N$	Number of Users
$d$	Dimension of feature vector
$U$	Feature vector set for Users
$A$	Feature vector set for Articles
$O_a$	Optimal Reward
$O_r$	Optimal Arm
$T$	Number of Iterations
$C$	Set of Cluster Centroids
${\mu }_u$	User feature vector for user u
${\nu }_u$	Article feature vector for article a

Figure 1. Convergence of cumulated regret

Figure 2. Accuracy of bandit parameter estimation

Table 2. Cumulated regret for $nusers=20$

alpha($\alpha$)	LinUCB	HybridLinUCB	CoLin
0.3	46.2468	22.2828	11.5598
0.2	21.1141	13.4912	11.5545
0.4	74.1557	31.0022	10.6086

Table 3. Cumulated regret for $nusers=10$

alpha	LinUCB	HybridLinUCB	CoLin
0.3	23.4665	9.9635	5.6060
0.2	11.8230	6.3285	6.1569
0.4	36.5001	13.1408	6.8308

Table 4. Cumulated regret for $nusers=40$

alpha($\alpha$)	LinUCB	HybridLinUCB	CoLin
0.3	344.4860	47.5695	34.1053
0.2	47.5195	31.6257	16.3011
0.4	133.7844	69.6611	19.8591

Figure 3. Accummulated regret (when k = 160)

Figure 4. Accummulated regret (when k = 80)

Table 5. Cumulated regret

No. of Clusters	LinUCB	HybridLinUCB	CoLin
40	344.4860	47.5695	34.1053
80	46.2468	22.2828	11.5598
160	74.1557	31.0022	10.6086

Figure 5. Convergence of accumulated regret

Table 6. Cumulated regret

LinUCB	HybridLinUCB	CoLin
90.04692	15.70729	8.950207

Figure 6. Optimum value of K in range (50 to 200)

Figure 7. Convergence of accumulated regret for alpha = 0.2

Figure 8. Convergence of accumulated regret for alpha = 0.3

Table 7. Table title 6 regret at $k=150$

alpha	LinUCB	HybridLinUCB	CoLin
0.2	2947.24	460.7695	266.7983
0.3	119.01	90.48	60.34