# Cooperative Attention-Based Learning between Diverse Data Sources
## 6 Model Limitations and Challenges
### Appendix B.2  
```
1. Initialize variables:  t = 0 (time step)  s_0 = initial state of the system  N = number of nodes  n = number of actions \(\omega\) = trade-off factor (0 to 1) \(\gamma\) = reward \(\pi\) = link reaction policy  h = actions history
2. Calculate reward for each node: \(\beta_{\pi^{i}}^{i,j}(s)=E\Big{[}\sum_{n=\gamma-1}^{t\geq 0,\,i,j\geq 0}\omega^{t} \gamma^{i,n}\big{(}s_{t}\times a^{n,t},\,s_{t+1}\big{)}\Big{|}a^{n,t\to j,t},x _{i}(t)\sim\pi(Event|s_{t}),\,s_{0}=s\Big{]}\)
3. Average reward to obtain global optima: \(\Big{[}\sum_{n>-1}^{t\geq 0}\omega\gamma\big{(}s_{t}\times a^{n,t},\,s_{t+1} \big{)},\Big{]}=0\)
4. Create link reaction policy: \(\pi(a|s):=\cap_{i\in N,\pi>-1,t\geq 0}\pi^{i,j}\Big{(}\frac{a^{n,t\to j,t}}{s_{t}}\Big{)}\)
5. Calculate optimal reward link: \(\beta_{\pi^{i}}^{i,j}(s)=E\Big{[}\sum_{n>-1}^{t\geq 0,\,i,j\geq 0}\omega^{t} \gamma^{j,n}\big{(}s_{t}\times a^{n,t},\,s_{t+1}\big{)}\Big{|}a^{n,t\to j,t},x_{i}(t)\sim\tau_{\pi^{i}}^{t},\,s_{0}=s\Big{]}\)
6. Calculate optimal join cooperative policy: \(\pi^{i,j}:s_{t}^{i,j}\to\Delta a^{n,t}\)
7. Update actions history: \(\tau_{\pi}^{t}=\prod\limits_{h:\beta_{\pi}^{i}\models h}\pi^{p(h^{t}|s_{t})}\)
8. Repeat steps 2 to 7 until terminal state is reached
```  
**Algorithm A2** Cooperative Learning and Strategy Creation Algorithm  
``` def spread_dynamic_variable(network, spread_rate, spread_time, spread_initial_nodes): spread_status = | for node in network_nodes: spread_status[node] = 0 for node in spread_initial_nodes: spread_status[node] = 1 for t in range(spread_time): for node in network_nodes: if spread_status[node] == 1: for neighbor in network_neighbors(node): if random.uniform(0, 1) < spread_rate: spread_status[neighbor] = 1 return spread_status

## References

* (1) [PERSON]; [PERSON]; [PERSON] Building a knowledge graph from natural language definitions for interpretable text entailment recognition. _arXiv_**2018**, arXiv:1806.07731. * (2) [PERSON]; [PERSON]; [PERSON]; [PERSON] The non-stochastic multi-armed bandit problem. _SIAM J. Comput._**2002**, _32_, 48-77. [CrossRef]
* (3) [PERSON]; [PERSON]; [PERSON] A review of evaluation techniques for social dialogue systems. In Proceedings of the 1 st ACM SIGCHI International Workshop on Investigating Social Interactions with Artificial Agents, New York, NY, USA, 13 November 2017; pp. 25-26. * (4) [PERSON]; [PERSON]; [PERSON] [PERSON] Neural machine translation by jointly learning to align and translate. _arXiv_**2014**, arXiv:1409.0473. * (5) [PERSON]; [PERSON] Information dissemination from social network for extreme weather scenario. _IEEE Trans. Comput. Soc. Syst._**2020**, \(7\), 319-328. [CrossRef]
* (6) [PERSON]; [PERSON]; [PERSON]; [PERSON] Reinforcement adaptation of an attention-based neural natural language generator for spoken dialogue systems. _Dialogue Discourse_**2019**, _10_, 1-19. [CrossRef]
* (7) [PERSON]; [PERSON] [PERSON]; [PERSON] Indirect reciprocity through gossiping can lead to cooperative clusters. In Proceedings of the 2011 IEEE Symposium on Artificial Life, Paris, France, 14 July 2011; pp. 154-161. * (8) [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON] Dynamical models explaining social balance and evolution of cooperation. _PLoS ONE_**2013**, \(8\), e60063. [CrossRef]
* (9) [PERSON]; [PERSON]; [PERSON] Detecting community structure in dynamic social networks using the concept of leadership. In _Sustainable Interdependent Networks_; Springer: Cham, Switzerland, 2018; pp. 97-118. * (10) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Drivers of emerging infectious disease events as a framework for digital detection. _Emerg. Infect. Dis._**2015**, _21_, 1285-1292. [CrossRef] [PubMed]
* (11) [PERSON]; [PERSON] On certain integrals of Lipschitz-Hankel type involving products of Bessel functions. _Philos. Trans. R. Soc. Lond._**1955**, _247_, 529-551. * (12) [PERSON]; [PERSON] Game dynamic model of social distancing while cost of infection varies with epidemic burden. _IMA J. Appl. Math._**2019**, _84_, 23-43.