Weihnachtsbaum

Merry Crispmas – Chapter 3: The Upside of a Local Minimum

The »Blackbox« already existed since the foundation of Seaborn. Some inhabitants even claim a longer time. Along with the marketplace, it was the central location for sociable and cozy evenings in the village, serving plain dishes accompanied with popular music. In its vaults, however, the tavern also offered room for some shady practice. The risk-seeking folk of Seaborn particularly loved to gamble. Looking for a thrill, it usually came down to a game of chance infamously called »Drawing without Replacement«. Many people lost everything but their spencer trying to master the compellingly risky game.
One of the cellars was filled with heated discussions: »We have to get rid of this son of a Bayesian! What a scrumbag…« shouted the tailor, clearly upset by the recent developments. »Oh Bud, leave it be!« The village elder tried to calm things down. »We should just make the best of the situation. There’s nothing we can do anyway. Let us simply focus on the final preparations«, he added with a certain voice. »We’re not going to let this halfwit ruin our celebration.«

Viewed from above, the scenery was mind-blowing.
He took three deep breaths, straightened up and let his eyes drift over his realm. Filling his lungs with air, he took a step towards the edge and screamed perfervidly. Everyone on Artificial Island should know of his happiness.
Accompanied by James, King Softmax took an extended expedition to scout the lands around Seaborn. They already left at dawn to climb the summit of Pearson Peak. Even though the course of the trail seemed to be simple and linear, they already lost valuable time on the ascent. In the morning fog, they got stuck in an inefficient loop through the woods – if not forever, they felt lost at least for an annoyingly long while. By now, the sun had already reached its turning point.
»Before Your Majesty starts building the residence, I would recommend some adjustments to optimize the current environment.« James was in his element, giving deliberate advice to the king. »Most importantly, we have to shrink the Random Forest. I would strongly advise reducing the number of trees. Secondly, the river’s current is way too unpredictable these days. We should minimize the risk of extreme flood events by smoothing the course of the stream. There’s still a lot of work ahead of us.«
»I appreciate your excellent consulting my dear James.« King Softmax looked confidently into the future. Over the course of the last weeks, he began to feel like a truly established ruler. »I’m sure this will become the residence we have always dreamed of.« Enjoying the last moments of silence on the summit of Pearson Peak, a satisfied smile stretched over their faces. What could possibly go wrong?

It knocked three times on the heavy wooden door. A high, slightly desperate voice was audible from outside: »Loretta?!«
Loretta removed the lock and cautiously opened the door. Before she could react, an agitated Mayor Pareta stormed past and instantly blurted out her sorrows.
»Loretta, you gotta help me. I just don’t know what to do. Everybody is acting like crazy.« Pareta was visibly out of breath but still sputtered like a waterfall. »Scrum down, my child.« Loretta tried to calm the mayor. »Take a cookie and have a seat by the fireplace. Claus, hand Pareta a cup of tea.« He greeted the mayor with a slightly bashful smile through his beard.
»Let’s start from scratch. What is it that bothers you, Pareta?« Eventually, the lady of herbs managed to calm down every troubled soul. After she found herself again, the mayor began to report on her misery. She told about the king’s plans, the villagers’ revolt and her personal predicament: »Oh dear, where shall I start? I’m just dissatisfied with the overall situation. After the proclamation unforeseen developments have taken overhand. Just now, I even was told that some folk gathered in the tavern to plan an uprising against the king. And did you hear that the king wants to attend the festivities tomorrow to solemnly announce everything himself? You see, Loretta, it’s all a huge mess…«
Loretta weighed her words and responded empathetically: »There, there, Pareta. Life is full of inflection points. But we have come up with a decent approach for all our problems so far, haven’t we? Just focus on the direction you’re heading to and not the size of your steps. No matter the learning rate, a robust optimizer will eventually converge to the optimal solution. Always remember the old saying of Seaborn:

When you feel to lose your socle,
stay patient till the iteration’s end.
Your minimum is only local.«

Chapter 4 will be published on the fourth Advent. Stay tuned!

<< Back to Chapter 2: The Preparations

Alexander Bauer (LMU München) und Johannes Stark (MHP)
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