To make optimal joint pricing and inventory control decisions is a critical challenge for modern retailers. In practice, retailers face changing market conditions where demands are influenced by various contextual factors, while simultaneously dealing with the difficulty of lost sales that obscure true demand information. However, existing approaches often fail to account for both contextual information and censored demand observations. We address this gap by presenting a framework where we model demand as a linear combination of basis functions with unknown coefficients, allowing for adaptive pricing and inventory decisions that respond to changing contexts. We propose an efficient algorithm to achieve regret bound O(KTlogT) under concave revenue conditions and O(K2/3T2/3(logT)1/2) for the general case, with matching lower bounds confirming optimality. Extensive numerical experiments across diverse scenarios demonstrate our algorithm's effectiveness.
Figures & tables
Paper
Context
Censored
Upper
Lower
Assumptions
Demand
Bound
Bound
( Chen et al., 2019 )
No
No
T
N/A
—
( Chen et al., 2021 )
No
Yes
T21+ν
N/A
logT -differentiable, concave
( Chen et al., 2024 )
No
Yes
T
N/A
Twice-differentiable, concave
( Chen et al., 2024 )
No
Yes
T53
T53
Twice-differentiable
Ours
Yes
Yes
T32
T32
Differentiable
Table 1: Comparison of Regret Bounds under Joint Pricing and Inventory Control Problems
θ^=argminθ∑t=1T0(ot−θ⊤ϕ(xt,pt))2
Algorithm 1 Joint Pricing and Inventory Control Algorithm with Censored Demand
Figure 1: Relative regret over time horizon T for different values of h and b .
Figure 2: Relative regret over time horizon T for different values of h and b (log-log scale).
Figure 3: Relative regret across different K values with standard deviation error bars.