## 7 Conclusion and Future Work  
In this paper, we address the problem of joint optimization of caching and recommendation for content delivery in IoT, which is NP-hard even even even for only one user and without considering recommendation. We consider the case where a recommendation is made among the cached contents, which is more general than assuming a recommendation is made only in accordance with users' preferences, as in the existing work. We solve this problem by splitting it into two subproblems: first, caching to maximize the total cache hit rate determined by user requests to all contents without considering recommendation, and then performing recommendation from the cached contents. We show that Subproblem 1 can be solved optimally by dynamic programming and Subproblem 2 possesses the submodular property, implying the existence of a solution with a performance guarantee of a worst-case approximation ratio to the optimal solution. Taking advantage of the properties of these two subproblems, we present a greedy algorithm to solve the problem of joint optimizationof cached recommendations that has a provable performance guarantee of \(1-\frac{1}{e}\). We experimentally validate the performance of our algorithm and demonstrate its hit rate improvement by simulation experiments and comparison with the most popular LFU algorithm. At the same time, we also show the variation patterns of hit rate measured by Jensen-Shannon Divergence on different parameter settings of cache capacity, \(\gamma\), \(\alpha\), and distortion limit \(d_{j}\). The results show that \(\gamma\), \(\alpha\), and \(d_{j}\) should be set appropriately to tradeoff the cache hit rate and user-preferred distortion. When recommendations are only made from cached content, it can reduce the frequency of obtaining content from the central server, thereby alleviating network bandwidth pressure. In environments where IoT device resources are limited, this assumption reduces network bandwidth pressure and has practical significance. In addition, we can cache the content that users may like in advance based on their browsing history. At this time, the cached content is closer to the user's actual preferences, and recommendations from the cached content will not deviate too far from the user's actual preferences. In addition, we use staged optimization with caching and recommendation, and we set caching based on the user's initial request preferences. However, recommendations change the probability distribution of user requests, and our cache optimization depends on the probability distribution of user requests, which may result in a cache that is not currently optimal after recommendations. If the cache optimization is redone, it will again lead to changes in the recommendation optimization. In practice, recommendation and caching need to be optimized alternately to obtain the best hit rate, and the caching and recommendation phases interact with each other, leading to the problem becoming an online, combinatorial optimization problem that needs to evolve over time, where each optimizationmust adapt to changing inputs caused by previous actions. The research of [PERSON] et al. [30] provides a class of dynamic combinatorial problems that accurately solve this kind of framework. In future work, we will combine their framework to optimize a two-stage greedy caching and recommendation optimization scheme into an online recurrent caching-recommendation alternation optimization scheme to enhance the robustness and applicability of our approach in dynamic environments of real-world applications. Conceptualization, H.S. ; Methodology, Z.L. ; Validation, H.T. ; Formal analysis, Z.L. and H.S. ; Investigation, Z.L. and H.T. ; Resources, H.S. ; Data curation, Z.L. ; Writing--original draft, Z.L. ; Writing--review & editing, H.S. and H.T. ; Supervision, H.S. All authors have read and agreed to the published version of the manuscript.