if we are within the feasible set already, we can do these to prevent us form getting out:

inequality constrained optimization

Generally things are of t]shape:

\begin{align} \min_{x}\quad & f_{0}\qty(x) \\ \textrm{s.t.} \quad & f_{i}\qty(x) \leq 0, i = 1\dots m \\ & Ax =b \end{align}

• convex, tie differentiable
• \(p^{*}\) is finite and attained
• strictly feasible

These include… LP, QP, QCQP, geometric program.

indicator barrier

Reformulate:

\begin{align} \min_{x}\quad & f_{0}\qty(x) + \sum_{i=1}^{m} I_{-}\qty(f_{i}\qty(x)) \\ \textrm{s.t.} \quad & Ax = b \end{align}

• Interior Point Method
• barrier method

Interior Point Method

How’s China Doing?

• overall: china’s growth is slowing
• property:
  • despite government support, property prices still struggling
  • falling demand => tighter financing => unfinished projects
• prices are going down—deflation!?

Involution (Neijuan)

• Dropping household wealth => more cautious purchasing.
• Young unemployment rate still elevated

Major Challenges

1. demogratic change
2. changing the growth model: state sector restructuring seems to have stopped
3. shifting to more domestic demand driven by consumers
4. changes in financial system—how can banks avoid over-lending
5. changes in fiscal system (how to find sources of revenue)
6. reducing corporate debt, LGFV debt, etc.

options are not great

• older model has had diminshing returns
• exports and trade surplus may not last
• more limited access to technologies and foreign direct investment
• high debt levels requires many years of debt logistics
• changes to population structure / aging limits consumptino and savings (so increasing domestic demand is hard)
• any fast shift to new growth model will bring a bit of depression

New Direction

1. maintain: focus on investment driven by state industrial policy
2. shift: investment from housing sector to optimized manufacturing (high tech)
3. expand: manufacturing capacity overall—but efficiency
4. double-down: on exports even if tariffs

ambitious and a huge gamble

Three layers of agent safety

1. model architecture: fundamental limitations of transformer structure
2. architecture -> LLMs: training data (poisoning), training objective (reward hacking)
3. LLMs -> prompts: prompt injections, unintended actions, goal scheming

prompt injections

OWASP top 10 for LLM applications…. RAG/Agents are WORSE because humans do not have choice. Web agents, can browse the web and have context poisoning.

evaluation setup

1. etiologic validity
2. realistic threat models
3. systematic evaluations (e.g., obviously anecdotal works)
4. controlled environments

computer security principles

• confidentiality (don’t infiltrate passwords)
• integrity (don’t nuke important files)
• availability (don’t bring things down)

benign inputs leading to harms

• triggering compaction => failures

Unintentional behavior: “unsafe agent behavior that deviations from user intentions from a task”