Model perception as information projection; use primal-dual to optimize data collection: minimize $\sum_j \textcolor{purple}{w_j} H(p_j|\textcolor{red}{a})$
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Entrepreneurs face operational decision-making under extreme uncertainty, without a clear structure for sequencing actions. We theorize this as a constrained optimization problem where the goal is to minimize stakeholder uncertainty $\textcolor{#3399FF}{U}$ given action costs $C$ and limited resources $\textcolor{#8B0000}{R}$. However, inferring the full venture state space $\textcolor{green}{S}$ (e.g., $5^{47}$ configurations) is computationally infeasible. To resolve this, we treat strategy as a hyperprior and actions as Bayesian updates, asking not “what can I do given my resources,” but rather, “what resources do I need to execute the optimal path.” This dual framing reverses inequality constraints into dynamic equalities that define reward distributions and resource requirements. Bottleneck breaking emerges as a middle-ground theory for actionable experimentation under structured tractability.
## relevant papers from [[đź“ťmoon24_csv_ai_cofounder]]
| Paper Title | Reason for Classification (Phase-Based Learning) | Optimization Component (3.1 Theoretical) |
| ------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| **Human–AI Collaboration Framework for Entrepreneurial Decision-Making** | Uses phased iteration to structurally lower operational uncertainty through stage-wise AI-supported decisions, clarifying sequential complexity​ | Defines structured state-action cogressively reduce operational uncertainty ($U_s$), explicitly shaping state transitions $D(S,A)=S'$​ |
| **Entrepreneurial Decision Model with Phase-Based Operational Uncertainty Reduction** | Proposes a clearly structured phase-based sequence for learning critical operisions, progressively reducing uncertainty by breaking down venture complexity into manageable phases . | Formalizes sequential decision-making as uncertainty minimization, explicitly guiding action selection across phases, refining state-action-utility relationships ($D(S,A)=S'$) . |
| **Integrative Models of Entrepreneurial Pivoting: A Simulation Approach** | Provides a simulated, phase-wise environment to test pivotal decisions, allowing entrepreneurs to systematically learn optimal operational strategies without real-world failure risks . | Clarifies theoretical uncertainty reduction through systematic scenario-testing, refining state-transition relationships ($D(S,A)=S'$) within phased action sequences . |
## ideas
using [[hier_mix.pdf]],
#### **Strategy as a hyperprior ($\textcolor{green}{\phi}$)**
Founders begin with a structured belief about what type of actions are likely to work across contexts—this is modeled as the **population-level hyperparameter** $\textcolor{green}{\phi}$ in a hierarchical Bayes model. Just as $\textcolor{green}{\phi}$ governs the distribution of traveler sensitivities ($\theta_n$) in the Swissmetro example, in entrepreneurship $\textcolor{green}{\phi}$ governs how founders assign prior likelihood to operational sequences like “collaborate first” vs. “segment first.” These priors may be informed by accelerators, mentors, or domain archetypes and encode strategy “style” at a meta level before any data ($y_n$) is observed. In this sense, the founder’s strategy reflects beliefs not about one venture, but about the distribution of decision pathways across similar ventures.
#### **Actions as Bayesian updates ($\textcolor{red}{a_t}$)**
Each entrepreneurial action $\textcolor{red}{a_t}$—e.g., applying to a testing facility or pitching to investors—yields observable outcomes analogous to $y_n$ in hierarchical Bayes models. These outcomes (e.g., stakeholder reactions, state transitions $S \rightarrow S'$) update the posterior over the founder’s latent decision parameters ($\theta$), narrowing uncertainty $U$ over time. Just as in the Swissmetro model we integrate over $f(\theta_n \mid \textcolor{green}{\phi})$ to get posterior likelihoods, here each action feeds into a posterior update conditioned on both prior strategic style ($\textcolor{green}{\phi}$) and current experimental evidence. This allows entrepreneurs to personalize their model based on partial feedback, learning over time what works best in their state-space.
Guided explicitly by gradients: $\frac{\nabla_{\textcolor{red}{A}}\textcolor{#3399FF}{U}(\textcolor{green}{S},\textcolor{red}{A})}{\textcolor{#FF69B4}{C}(\textcolor{red}{A})}$, maximizing utility per unit cost explicitly across stakeholders.
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two 🍾bottleneck breaking
- 🍾 first, between NAIL and SCALE where innovation's value is much higher than operational efficiency's value.
- 🍾🍾second, between actions within NAIL reaching to 1,1,1 meaning value proposition accepted by three stakeholders
# Optimization Formulation Table
|Variable|Definition|Example with Sublime Systems (Cement Company)|
|---|---|---|
|W (Weight Vector)|Importance weights assigned to each stakeholder (customer, operations partner, investor)|For Sublime Systems: W_customer might be higher than typical since decarbonizing cement is a priority for construction companies due to environmental regulations|
|U (Uncertainty Vector)|Residual uncertainty about whether each stakeholder will accept the venture's value proposition|For Sublime Systems: Uncertainty about whether testing facilities will approve their low-carbon cement, whether construction companies will adopt it, and whether investors will fund it|
|S (State Vector)|Binary representation of stakeholder acceptance (1) or non-acceptance (0) for customer, operations partner, and investor|Initial state might be (0,0,0) with the goal to reach (1,1,1) where all stakeholders accept|
|A (Action Vector)|Entrepreneur's decisions on whether to segment (marketing), collaborate (operations), or capitalize (fundraising)|For Sublime Systems: Deciding to focus first on collaborating with cement testing facilities|
|B (State to Uncertainty)|Matrix mapping the current state to uncertainty levels for each stakeholder|For cement company: Lower uncertainty for customers (building constructors) who are under pressure to reduce carbon footprint|
|C (Action to Cost)|Matrix mapping actions to resource requirements or costs|For Sublime Systems: Collaborating with testing facilities might have lower cost if they have connections|
|D (State Transition)|Matrix showing how actions affect state transitions|For materials company: Getting approval from testing facility (collaboration) might have spillover effect, improving chances with customers by 20%|
|R (Resources)|Available resources for the venture to use in actions|Sublime Systems' available capital, time, and connections to pursue actions|
## Understanding the Database to Matrix Mapping
Based on the transcript discussions and the database layout provided, I can now propose how the existing database structure would map to the optimization variables (B, C, D matrices) in the Bayesian entrepreneurship model.
### Mapping from Database to B Matrix (State to Uncertainty)
The B matrix represents how a venture's state impacts uncertainty across stakeholders. From the database:
- **CustomerValueProposition** table: Contains information about industry, venture type, and value proposition that would affect customer uncertainty
- **FounderBackground** table: Experience and background that would affect investor uncertainty
- **StartupJourney** table: Success indicators that would affect all stakeholder uncertainties
### Mapping from Database to C Matrix (Action to Cost)
The C matrix represents the cost of various actions (segment, collaborate, capitalize). From the database:
- **Funding** table: Contains information on resources available (total_amount_raised, latest_valuation)
- **Marketing** table: Represents some segmentation costs through marketing channels
- **StartupJourney**: number_of_pivots can indicate previous action costs
### Mapping from Database to D Matrix (State Transition)
The D matrix represents how actions change the venture's state. This is the most complex and might require additional data not currently in the database:
- **StartupJourney**: within_3_years_success and post_three_years_success could help derive historical transition probabilities
- **Funding**: funding rounds progression could show state transitions following capitalization actions
### Step 2: Mapping Operational and Stakeholder Uncertainty with Matrices (B, C, D)
| Dimension | Mathematical Structure | Meaning (10-year-old) | Examples (Top 3 ordered by helpfulness) | Matrix Mapping (Intuition) |
| --------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| **Operational Uncertainty** | $D[i,\textcolor{red}{a},\textcolor{green}{s},\textcolor{green}{s'}]$: uncertainty about **when** and **how fast** states change. | "Not knowing when or how fast things will happen." | 1. Time to receive approval from third-party testing lab (e.g., ASTM)<br>2. Time to scale lab-to-field cement formulation<br>3. Duration of government permitting process for demo deployment | [[I.📽️Perception Decision Framework]] <br><br>sort by wU/C<br><br>**$C$ (Action-resource linkage) **Maps action $\textcolor{red}{a}$ to resource cost $\textcolor{#8B0000}{R}$—founders know these best and report them directly. <br><br>[[III.⚡Bottleneck-Driven Action Sequencing]]<br><br>**$D$ (Dynamic consistency)**Captures how chosen actions (e.g., apply to testing lab) probabilistically lead to future states (e.g., feasibility accepted). Essential to planning sequential moves like moving from prototype to pilot stage. |
| **Stakeholder Uncertainty** | Non-linear, discrete interactions in $\Delta\textcolor{#3399FF}{U_j}$, and $C(\textcolor{red}{a})$: uncertainty about **which actions fit together best**, and their interactions at a given moment. | "Not knowing exactly where things fit or which actions go well together." | 1. Whether approval from testing lab increases investor interest<br>2. Whether early customer interest translates to operational collaboration<br>3. Whether securing a VC commitment helps unlock supplier partnerships | [[II.🔄Multi-Stakeholder Decision Matrices]]<br><br>**$B$ (State-to-uncertainty linkage)**Maps current stakeholder acceptances to residual uncertainty (e.g., if ops partner hasn't said yes, $\textcolor{#3399FF}{U_s}$ remains high).<br> |